47 results on '"Robust testing"'
Search Results
2. Testing Equality of Multiple Population Means under Contaminated Normal Model Using the Density Power Divergence.
- Author
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Das, Jagannath, Beyaztas, Beste Hamiye, Mac-Ocloo, Maxwell Kwesi, Majumdar, Arunabha, and Mandal, Abhijit
- Subjects
- *
POWER density , *ONE-way analysis of variance , *FALSE positive error , *BONE marrow - Abstract
This paper considers the problem of comparing several means under the one-way Analysis of Variance (ANOVA) setup. In ANOVA, outliers and heavy-tailed error distribution can seriously hinder the treatment effect, leading to false positive or false negative test results. We propose a robust test of ANOVA using an M-estimator based on the density power divergence. Compared with the existing robust and non-robust approaches, the proposed testing procedure is less affected by data contamination and improves the analysis. The asymptotic properties of the proposed test are derived under some regularity conditions. The finite-sample performance of the proposed test is examined via a series of Monte-Carlo experiments and two empirical data examples—bone marrow transplant dataset and glucose level dataset. The results produced by the proposed testing procedure are favorably compared with the classical ANOVA and robust tests based on Huber's M-estimator and Tukey's MM-estimator. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
3. Semi-Automatic Generation of Cognitive Science Theories
- Author
-
Addis, Mark, Gobet, Fernand, Lane, Peter C. R., Sozou, Peter D., Bueno, Otávio, Editor-in-Chief, Brogaard, Berit, Editorial Board Member, Chakravartty, Anjan, Editorial Board Member, French, Steven, Editorial Board Member, Dutilh Novaes, Catarina, Editorial Board Member, Addis, Mark, editor, Lane, Peter C. R., editor, Sozou, Peter D., editor, and Gobet, Fernand, editor
- Published
- 2019
- Full Text
- View/download PDF
4. Tests and estimation strategies associated to some loss functions.
- Author
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Baraud, Yannick
- Subjects
- *
RANDOM variables , *DATA distribution , *BAYES' estimation , *INDEPENDENT variables , *PROBABILITY theory , *DATABASES - Abstract
We consider the problem of estimating the joint distribution of n independent random variables. Given a loss function and a family of candidate probabilities, that we shall call a model, we aim at designing an estimator with values in our model that possesses good estimation properties not only when the distribution of the data belongs to the model but also when it lies close enough to it. The losses we have in mind are the total variation, Hellinger, Wasserstein and L p -distances to name a few. We show that the risk of our estimator can be bounded by the sum of an approximation term that accounts for the loss between the true distribution and the model and a complexity term that corresponds to the bound we would get if this distribution did belong to the model. Our results hold under mild assumptions on the true distribution of the data and are based on exponential deviation inequalities that are non-asymptotic and involve explicit constants. Interestingly, when the model reduces to two distinct probabilities, our procedure results in a robust test whose errors of first and second kinds only depend on the losses between the true distribution and the two tested probabilities. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
5. Testing Equality of Multiple Population Means under Contaminated Normal Model Using the Density Power Divergence
- Author
-
Jagannath Das, Beste Hamiye Beyaztas, Maxwell Kwesi Mac-Ocloo, Arunabha Majumdar, and Abhijit Mandal
- Subjects
minimum density power divergence ,robust ANOVA ,fixed effects ,robust testing ,M-estimation ,Science ,Astrophysics ,QB460-466 ,Physics ,QC1-999 - Abstract
This paper considers the problem of comparing several means under the one-way Analysis of Variance (ANOVA) setup. In ANOVA, outliers and heavy-tailed error distribution can seriously hinder the treatment effect, leading to false positive or false negative test results. We propose a robust test of ANOVA using an M-estimator based on the density power divergence. Compared with the existing robust and non-robust approaches, the proposed testing procedure is less affected by data contamination and improves the analysis. The asymptotic properties of the proposed test are derived under some regularity conditions. The finite-sample performance of the proposed test is examined via a series of Monte-Carlo experiments and two empirical data examples—bone marrow transplant dataset and glucose level dataset. The results produced by the proposed testing procedure are favorably compared with the classical ANOVA and robust tests based on Huber’s M-estimator and Tukey’s MM-estimator.
- Published
- 2022
- Full Text
- View/download PDF
6. Review on Testing of Cyber Physical Systems: Methods and Testbeds
- Author
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Xin Zhou, Xiaodong Gou, Tingting Huang, and Shunkun Yang
- Subjects
Cyber-physical system ,non-functional testing ,robust testing ,security testing ,testing method ,testbed ,Electrical engineering. Electronics. Nuclear engineering ,TK1-9971 - Abstract
Cyber physical systems (CPSs) are rapidly developing, with increasing scale, complexity and heterogeneity. However, testing CPSs systematically to ensure that they operate with high reliability remains a big challenge. Therefore, it is necessary to summarize existing works and technologies systematically, with the aim of inspiring new inventions for more efficient CPS testing. Accordingly, this paper first investigated the advances in CPS testing methods from ten aspects, including different testing paradigms, technologies, and some non-functional testing methods (including security testing, robust testing, and fragility testing). Then, we further elaborate on the infrastructures of CPS testbeds from the perspectives of their architecture and the corresponding function analyses. Finally, challenges and future research directions are identified and discussed. It can be concluded that future CPS testing should focus more on the combination of different paradigms and technologies for multi-objective by integrating more emerging cutting-edge technologies such as Internet of things, big data, cloud computing and AI.
- Published
- 2018
- Full Text
- View/download PDF
7. Robust Testing of Cascading Failure Mitigations Based on Power Dispatch and Quick-Start Storage.
- Author
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Xu, Zhe, Julius, A. Agung, and Chow, Joe H.
- Abstract
We present a formal robust testing method for power system cascading failure mitigations. The approach is model-based, using simulated trajectories of the system and proving that uncertainties, e.g., in the initial states or disturbances, do not perturb the trajectories beyond a robust neighborhood around them. We model power systems as hybrid systems with locations representing different swing dynamics and relay dynamics. We present implementations of our robust testing approach in a three-machine system model from the 2003 Italian Blackout and the IEEE 39-bus system model. We apply the robust testing method in two scenarios for averting the cascading failures: 1) robust testing of safety for various generator mechanical power dispatch schedules and 2) robust testing of safety for postfault remedial actions based on quick-start storage. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
8. Robust inference for seemingly unrelated regression models.
- Author
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Peremans, Kris and Van Aelst, Stefan
- Subjects
- *
ROBUST control , *ESTIMATION theory , *REGRESSION analysis , *STATISTICAL bootstrapping , *SIMULATION methods & models - Abstract
Seemingly unrelated regression models generalize linear regression models by considering multiple regression equations that are linked by contemporaneously correlated disturbances. Robust inference for seemingly unrelated regression models is considered. MM-estimators are introduced to obtain estimators that have both a high breakdown point and a high normal efficiency. A fast and robust bootstrap procedure is developed to obtain robust inference for these estimators. Confidence intervals for the model parameters as well as hypothesis tests for linear restrictions of the regression coefficients in seemingly unrelated regression models are constructed. Moreover, in order to evaluate the need for a seemingly unrelated regression model, a robust procedure is proposed to test for the presence of correlation among the disturbances. The performance of the fast and robust bootstrap inference is evaluated empirically in simulation studies and illustrated on real data. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
9. A robust audio classification system for detecting pulmonary edema.
- Author
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Hong, K.J., Essid, S., Ser, W., and Foo, D.C.-g.
- Subjects
PULMONARY edema ,ACOUSTIC signal processing ,FEATURE selection ,ROBUST control ,SUPPORT vector machines ,DIAGNOSIS - Abstract
Abstract In this paper we present a robust audio classification system to efficiently detect pulmonary edema. The system uses a feature learning technique based on (NMF), then classified with logistic regression. A study was done to compare feature engineering approaches with feature selection techniques against NMF. Different NMF schemes were investigated and also compared with Principal Component Analysis. NMF scored 95% F1 score, which was superior to feature engineering techniques that had scores from 83% to 93%. Background noise collected from hospitals and speech from a speech corpus database was used to simulate noisy data. The system was then tested using noisy data. The best NMF scheme scored 74%, while other feature engineering techniques scored lower; from 66% to 71%. NMF was also used as a signal enhancement tool. It improved the F1 score to 77%. Lastly, only inhalations from breath sounds were considered and this further improved classification results to 86%. The proposed robust classification system using NMF thus proved to be an effective method for audio-based detection of pulmonary edema. If implemented in real-time, the proposed system can be used as a screening tool. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
10. Robust Test Generation and Coverage for Hybrid Systems
- Author
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Julius, A. Agung, Fainekos, Georgios E., Anand, Madhukar, Lee, Insup, Pappas, George J., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Rangan, C. Pandu, editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Bemporad, Alberto, editor, Bicchi, Antonio, editor, and Buttazzo, Giorgio, editor
- Published
- 2007
- Full Text
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11. Likelihood Ratio Testing under Measurement Errors
- Author
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Michel Broniatowski, Jana Jurečková, and Jan Kalina
- Subjects
measurement errors ,robust testing ,two-sample test ,misspecified hypothesis and alternative ,2-alternating capacities ,Science ,Astrophysics ,QB460-466 ,Physics ,QC1-999 - Abstract
We consider the likelihood ratio test of a simple null hypothesis (with density f 0 ) against a simple alternative hypothesis (with density g 0 ) in the situation that observations X i are mismeasured due to the presence of measurement errors. Thus instead of X i for i = 1 , … , n , we observe Z i = X i + δ V i with unobservable parameter δ and unobservable random variable V i . When we ignore the presence of measurement errors and perform the original test, the probability of type I error becomes different from the nominal value, but the test is still the most powerful among all tests on the modified level. Further, we derive the minimax test of some families of misspecified hypotheses and alternatives. The test exploits the concept of pseudo-capacities elaborated by Huber and Strassen (1973) and Buja (1986). A numerical experiment illustrates the principles and performance of the novel test.
- Published
- 2018
- Full Text
- View/download PDF
12. Robust asymptotic tests for the equality of multivariate coefficients of variation.
- Author
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Aerts, Stephanie and Haesbroeck, Gentiane
- Abstract
In order to easily compare several populations on the basis of more than one feature, multivariate coefficients of variation (MCV) may be used as they allow to summarize relative dispersion in a single index. However, up to date, no test of equality of one or more MCVs has been developed in the literature. In this paper, several classical and robust Wald-type tests are proposed and studied. The asymptotic distributions of the test statistics are derived under elliptical symmetry, and the asymptotic efficiency of the robust versions is compared to the classical tests. Robustness of the proposed procedures is examined through partial and joint influence functions of the test statistic, as well as by means of power and level influence functions. A simulation study compares the performance of the classical and robust tests under uncontaminated and contaminated schemes, and the difference with the usual covariance homogeneity test is highlighted. As a by-product, these tests may also be considered in the univariate context where they yield procedures that are both robust and easy-to-use. They provide an interesting alternative to the numerous parametric tests existing in the literature, which are, in most cases, unreliable in presence of outliers. The methods are illustrated on a real data set. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
13. A Procedure for Robust Estimation and Inference in Linear Regression
- Author
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Yohai, Victor J., Stahel, Werner A., Zamar, Ruben H., Friedman, Avner, editor, Miller, Willard, Jr., editor, Stahel, Werner, and Weisberg, Sanford
- Published
- 1991
- Full Text
- View/download PDF
14. Performance hypothesis testing with the Sharpe ratio: The case of hedge funds.
- Author
-
Auer, Benjamin R. and Schuhmacher, Frank
- Abstract
Highlights: [•] We provide a Sharpe ratio based performance analysis of the hedge fund market. [•] We analyse whether the choice of test can influence an investor’s fund selection. [•] Our results show only a small percentage of significant outperformers. [•] The choice of statistical test crucially influences this outcome. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
15. Improving the bandwidth-free inference methods by prewhitening.
- Author
-
Rho, Yeonwoo and Shao, Xiaofeng
- Subjects
- *
BANDWIDTHS , *MATHEMATICAL statistics , *TIME series analysis , *REGRESSION analysis , *HETEROSCEDASTICITY , *AUTOCORRELATION (Statistics) , *PARAMETER estimation - Abstract
Abstract: In this paper we consider inference of parameters in time series regression models. In the traditional inference approach, the heteroskedasticity and autocorrelation consistent (HAC) estimation is often involved to consistently estimate the asymptotic covariance matrix of regression parameter estimator. Since the bandwidth parameter in the HAC estimation is difficult to choose in practice, there has been a recent surge of interest in developing bandwidth-free inference methods. However, existing simulation studies show that these new methods suffer from severe size distortion in the presence of strong temporal dependence for a medium sample size. To remedy the problem, we propose to apply the prewhitening to the inconsistent long-run variance estimator in these methods to reduce the size distortion. The asymptotic distribution of the prewhitened Wald statistic is obtained and the general effectiveness of prewhitening is shown through simulations. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
16. Review on Testing of Cyber Physical Systems: Methods and Testbeds
- Author
-
Zhou Xin, Shunkun Yang, Xiaodong Gou, and Tingting Huang
- Subjects
non-functional testing ,0209 industrial biotechnology ,security testing ,General Computer Science ,Computer science ,media_common.quotation_subject ,Big data ,Cloud computing ,02 engineering and technology ,Security testing ,Cyber-physical system ,testbed ,Data modeling ,020901 industrial engineering & automation ,Unified Modeling Language ,0202 electrical engineering, electronic engineering, information engineering ,General Materials Science ,Function (engineering) ,computer.programming_language ,media_common ,robust testing ,testing method ,business.industry ,Scale (chemistry) ,General Engineering ,Data science ,020201 artificial intelligence & image processing ,lcsh:Electrical engineering. Electronics. Nuclear engineering ,business ,lcsh:TK1-9971 ,computer - Abstract
Cyber physical systems (CPSs) are rapidly developing, with increasing scale, complexity, and heterogeneity. However, testing CPSs systematically to ensure that they operate with high reliability remains a big challenge. Therefore, it is necessary to summarize existing works and technologies systematically, with the aim of inspiring new inventions for more efficient CPS testing. Accordingly, this paper first investigated the advances in CPS testing methods from ten aspects, including different testing paradigms, technologies, and some non-functional testing methods (including security testing, robust testing, and fragility testing). Then, we further elaborate on the infrastructures of CPS testbeds from the perspectives of their architecture and the corresponding function analyses. Finally, challenges and future research directions are identified and discussed. It can be concluded that future CPS testing should focus more on the combination of different paradigms and technologies for multi-objective by integrating more emerging cutting-edge technologies such as Internet of things, big data, cloud computing, and AI.
- Published
- 2018
17. Robust nonparametric detection of objects in noisy images.
- Author
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Langovoy, Mikhail and Wittich, Olaf
- Subjects
- *
NOISE , *ROBUST control , *NONPARAMETRIC estimation , *PERCOLATION theory , *RANDOM graphs , *ALGORITHMS , *IMAGE analysis , *MATHEMATICAL proofs - Abstract
We propose a novel statistical hypothesis testing method for the detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our testing procedure. In addition, we address not only an asymptotic behaviour of the method, but also a finite sample performance of our test. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
18. From Local to Robust Testing via Agreement Testing
- Author
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Irit Dinur and Prahladh Harsha and Tali Kaufman and Noga Ron-Zewi, Dinur, Irit, Harsha, Prahladh, Kaufman, Tali, Ron-Zewi, Noga, Irit Dinur and Prahladh Harsha and Tali Kaufman and Noga Ron-Zewi, Dinur, Irit, Harsha, Prahladh, Kaufman, Tali, and Ron-Zewi, Noga
- Abstract
A local tester for an error-correcting code is a probabilistic procedure that queries a small subset of coordinates, accepts codewords with probability one, and rejects non-codewords with probability proportional to their distance from the code. The local tester is robust if for non-codewords it satisfies the stronger property that the average distance of local views from accepting views is proportional to the distance from the code. Robust testing is an important component in constructions of locally testable codes and probabilistically checkable proofs as it allows for composition of local tests. In this work we show that for certain codes, any (natural) local tester can be converted to a roubst tester with roughly the same number of queries. Our result holds for the class of affine-invariant lifted codes which is a broad class of codes that includes Reed-Muller codes, as well as recent constructions of high-rate locally testable codes (Guo, Kopparty, and Sudan, ITCS 2013). Instantiating this with known local testing results for lifted codes gives a more direct proof that improves some of the parameters of the main result of Guo, Haramaty, and Sudan (FOCS 2015), showing robustness of lifted codes. To obtain the above transformation we relate the notions of local testing and robust testing to the notion of agreement testing that attempts to find out whether valid partial assignments can be stitched together to a global codeword. We first show that agreement testing implies robust testing, and then show that local testing implies agreement testing. Our proof is combinatorial, and is based on expansion / sampling properties of the collection of local views of local testers. Thus, it immediately applies to local testers of lifted codes that query random affine subspaces in F_q^m, and moreover seems amenable to extension to other families of locally testable codes with expanding families of local views.
- Published
- 2019
- Full Text
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19. A review and some new results on permutation testing for multivariate problems.
- Author
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Pesarin, Fortunato and Salmaso, Luigi
- Abstract
In recent years permutation testing methods have increased both in number of applications and in solving complex multivariate problems. When available permutation tests are essentially of an exact nonparametric nature in a conditional context, where conditioning is on the pooled observed data set which is often a set of sufficient statistics in the null hypothesis. Whereas, the reference null distribution of most parametric tests is only known asymptotically. Thus, for most sample sizes of practical interest, the possible lack of efficiency of permutation solutions may be compensated by the lack of approximation of parametric counterparts. There are many complex multivariate problems, quite common in empirical sciences, which are difficult to solve outside the conditional framework and in particular outside the method of nonparametric combination (NPC) of dependent permutation tests. In this paper we review such a method and its main properties along with some new results in experimental and observational situations (robust testing, multi-sided alternatives and testing for survival functions). [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
20. Accurately sized test statistics with misspecified conditional homoskedasticity.
- Author
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Erb, Jack and Steigerwald, Douglas G.
- Subjects
- *
MATHEMATICAL statistics , *REGRESSION analysis , *ERRORS , *AUTOCORRELATION (Statistics) , *CONFIDENCE intervals , *ESTIMATION theory , *SIMULATION methods & models , *BANDWIDTHS - Abstract
We study the finite-sample performance of test statistics in linear regression models where the error dependence is of unknown form. With an unknown dependence structure, there is traditionally a trade-off between the maximum lag over which the correlation is estimated (the bandwidth) and the amount of heterogeneity in the process. When allowing for heterogeneity, through conditional heteroskedasticity, the correlation at far lags is generally omitted and the resultant inflation of the empirical size of test statistics has long been recognized. To allow for correlation at far lags, we study the test statistics constructed under the possibly misspecified assumption of conditional homoskedasticity. To improve the accuracy of the test statistics, we employ the second-order asymptotic refinement in Rothenberg [Approximate power functions for some robust tests of regression coefficients, Econometrica 56 (1988), pp. 997-1019] to determine the critical values. The simulation results of this paper suggest that when sample sizes are small, modelling the heterogeneity of a process is secondary to accounting for dependence. We find that a conditionally homoskedastic covariance matrix estimator (when used in conjunction with Rothenberg's second-order critical value adjustment) improves test size with only a minimal loss in test power, even when the data manifest significant amounts of heteroskedasticity. In some specifications, the size inflation was cut by nearly 40% over the traditional heteroskedasticity and autocorrelation consistent (HAC) test. Finally, we note that the proposed test statistics do not require that the researcher specify the bandwidth or the kernel. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
21. Robust tests based on dual divergence estimators and saddlepoint approximations
- Author
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Toma, Aida and Leoni-Aubin, Samuela
- Subjects
- *
ROBUST statistics , *ESTIMATION theory , *METHOD of steepest descent (Numerical analysis) , *STATISTICAL hypothesis testing , *ASYMPTOTIC theory in regression analysis , *MATHEMATICAL models - Abstract
Abstract: This paper is devoted to robust hypothesis testing based on saddlepoint approximations in the framework of general parametric models. As is known, two main problems can arise when using classical tests. First, the models are approximations of reality and slight deviations from them can lead to unreliable results when using classical tests based on these models. Then, even if a model is correctly chosen, the classical tests are based on first order asymptotic theory. This can lead to inaccurate -values when the sample size is moderate or small. To overcome these problems, robust tests based on dual divergence estimators and saddlepoint approximations, with good performances in small samples, are proposed. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
- View/download PDF
22. Resampling schemes with low resampling intensity and their applications in testing hypotheses
- Author
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del Barrio, Eustasio, Janssen, Arnold, and Matrán, Carlos
- Subjects
- *
RESAMPLING (Statistics) , *STATISTICAL bootstrapping , *PERMUTATIONS , *REGRESSION analysis , *NONPARAMETRIC statistics , *STATISTICAL hypothesis testing - Abstract
Abstract: The paper explores statistical features of different resampling schemes under low resampling intensity. The original sample is considered in a very general framework of triangular arrays, without independence or equally distributed assumptions, although improvements under such conditions are also provided. We show that low resampling schemes have very interesting and flexible properties, providing new insights into the performance of widely used resampling methods, including subsampling, two-sample unbalanced permutation statistics or wild bootstrap. It is shown that, under regularity assumptions, resampling tests with critical values derived by the appertaining low resampling procedures are asymptotically valid and there is no loss of power compared with the power function of an ideal (but unfeasible) parametric family of tests. Moreover we show that in several contexts, including regression models, they may act as a filter for the normal part of a limit distribution, turning down the influence of outliers. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
23. Some suggestions about appropriate use of the Kruskal–Wallis test
- Author
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Ruxton, Graeme D. and Beauchamp, Guy
- Published
- 2008
- Full Text
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24. Robust testing with generalized partial linear models for longitudinal data
- Author
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Zhou, Jianhui, Zhu, Zhongyi, and Fung, Wing K.
- Subjects
- *
NONPARAMETRIC statistics , *REGRESSION analysis , *ESTIMATION theory , *LONGITUDINAL method , *ASYMPTOTIC distribution - Abstract
Abstract: By approximating the nonparametric component using a regression spline in generalized partial linear models (GPLM), robust generalized estimating equations (GEE), involving bounded score function and leverage-based weighting function, can be used to estimate the regression parameters in GPLM robustly for longitudinal data or clustered data. In this paper, score test statistics are proposed for testing the regression parameters with robustness, and their asymptotic distributions under the null hypothesis and a class of local alternative hypotheses are studied. The proposed score tests reply on the estimation of a smaller model without the testing parameters involved, and perform well in the simulation studies and real data analysis conducted in this paper. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
25. Testing Variability in the Two-Sample Case.
- Author
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Ramsey, PhilipH. and Ramsey, PatriciaP.
- Subjects
- *
ROBUST statistics , *DISTRIBUTION (Probability theory) , *MATHEMATICAL statistics , *STATISTICAL sampling , *STATISTICS - Abstract
A number of robust methods for testing variability have been reported in previous literature. An examination of these procedures for a wide variety of populations confirms their general robustness. Shoemaker's improvement of the F test extends that test use to a realistic variety of population shapes. However, a combination of the Brown-Forsythe and O'Brien methods based on testing kurtosis is shown to be conservative for a wide range of sample sizes and population distributions. The composite test is also shown to be more powerful in most conditions than other conservative procedures. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
26. Optimal Conditionally Unbiased Bounded-Influence Inference in Dynamic Location and Scale Models.
- Author
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Mancini, Loriano, Ronchetti, Elvezio, and Trojani, Fabio
- Subjects
- *
ESTIMATION theory , *MONTE Carlo method , *HETEROSCEDASTICITY , *ECONOMETRICS , *GAUSSIAN processes , *ALGORITHMS - Abstract
This article studies the local robustness of estimators and tests for the conditional location and scale parameters in a strictly stationary time series model. We first derive optimal bounded-influence estimators for such settings under a conditionally Gaussian reference model. Based on these results, we obtain optimal bounded-influence versions of the classical likelihood-based tests for parametric hypotheses. We propose a feasible and efficient algorithm for the computation of our robust estimators, which uses analytical Laplace approximations to estimate the auxiliary recentering vectors, ensuring Fisher consistency in robust estimation. This strongly reduces the computation time by avoiding the simulation of multidimensional integrals, a task that typically must be addressed in the robust estimation of nonlinear models for time series. In some Monte Carlo simulations of an AR( 1 )-ARCH( 1) process, we show that our robust procedures maintain a very high efficiency under ideal model conditions and at the same time perform very satisfactorily under several forms of departure from conditional normality. In contrast, classical pseudo-maximum likelihood inference procedures are found to be highly inefficient under such local model misspecifications. These patterns are confirmed by an application to robust testing for autoregressive conditional heteroscedasticity. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
27. Minimum value assured by a method to determine gold in alloys by using laser-induced breakdown spectroscopy and partial least-squares calibration model
- Author
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Ortiz, M.C., Sarabia, L., Jurado-López, A., and Luque de Castro, M.D.
- Subjects
- *
GOLD , *JEWELRY , *SPECTRUM analysis , *LEAST squares - Abstract
A procedure for estimating the minimum value assured by an analytical method has been developed. It is applied to the determination of gold in jewellery alloys by means of a recently proposed spectroscopy technique. The laser-induced breakdown spectroscopic data of 17 gold alloys, with gold concentration ranging between 50 and 100% were used as calibration set for carrying out the partial least-squares regression (PLS). Ninety alloys, with known gold concentration, were used to evaluate the method’s accuracy. Finally, the minimum guaranteed value of the gold content was analysed, taking into account the values for gold hallmark in Spanish regulations. [Copyright &y& Elsevier]
- Published
- 2004
- Full Text
- View/download PDF
28. Robust tests in generalized linear models with missing responses.
- Author
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Bianco, Ana M., Boente, Graciela, and Rodrigues, Isabel M.
- Subjects
- *
ROBUST control , *GENERALIZATION , *LINEAR statistical models , *DATA analysis , *STATISTICS , *ASYMPTOTIC distribution - Abstract
Abstract: In many situations, data follow a generalized linear model in which the mean of the responses is modelled, through a link function, linearly on the covariates. Robust estimators for the regression parameter in order to build test statistics for this parameter, when missing data occur in the responses, are considered. The asymptotic behaviour of the robust estimators for the regression parameter is obtained, under the null hypothesis and under contiguous alternatives. This allows us to derive the asymptotic distribution of the robust Wald-type test statistics constructed from the proposed estimators. The influence function of the test statistics is also studied. A simulation study allows us to compare the behaviour of the classical and robust tests, under different contamination schemes. Applications to real data sets enable to investigate the sensitivity of the -value to the missing scheme and to the presence of outliers. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
29. Testing in generalized partially linear models: A robust approach
- Author
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Boente, Graciela, Cao, Ricardo, González Manteiga, Wenceslao, and Rodriguez, Daniela
- Subjects
- *
LINEAR statistical models , *STATISTICAL hypothesis testing , *ROBUST control , *MATHEMATICAL models , *SMOOTHNESS of functions , *NONLINEAR statistical models , *MAXIMUM likelihood statistics - Abstract
Abstract: In this paper, we introduce a family of robust statistics which allow to decide between a parametric model and a semiparametric one. More precisely, under a generalized partially linear model, i.e., when the observations satisfy with and a known link function, we want to test against is a nonlinear smooth function. A general approach which includes robust estimators based on a robustified deviance or a robustified quasi-likelihood is considered. The asymptotic behavior of the test statistic under the null hypothesis is obtained. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
30. On Reasons for Introducing Means for Approximately Optimal Choice of Robust Procedure
- Author
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Víšek, Jan Ámos, Kubík, Stanislav, editor, Víšek, Jan Ámos, editor, and Vísek, J. A.
- Published
- 1988
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31. Robust Recursive Estimation and Detection of Shifts in Regression
- Author
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Kuh, E., Samarov, A., De Antoni, F., editor, Lauro, N., editor, and Rizzi, A., editor
- Published
- 1986
- Full Text
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32. Robust Wald-type methods for testing equality between two populations regression parameters: A comparative study under the logistic model.
- Author
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Bianco, Ana M., Boente, Graciela, and Rodrigues, Isabel M.
- Subjects
- *
PARAMETERS (Statistics) , *TEST methods , *COMPARATIVE studies , *MATHEMATICAL equivalence , *DATA analysis - Abstract
Comparing the regression parameters between two populations is useful to understand the homogeneity of the process underlying the data. The problem of logistic regression is considered when the practitioner handles data from two populations and when the goal is to test the hypothesis that some regression parameters are equal in both populations. A classical testing procedure is to construct a Wald-type test from the maximum likelihood estimators obtained from each data set. However, as in the one-population setting, the presence of outliers in any of the two samples may distort both the level and/or the power of this procedure. Instead of the maximum likelihood procedure, reliable statistics are built using a class of robust estimators which bound large values of the deviance as well as the effect of high leverage points. The asymptotic behaviour of this family of test statistics is derived under the null and contiguous alternatives. Besides, the robustness of the tests is investigated through the influence function. A simulation study allows to compare, under different contamination schemes, the behaviour of the tests based on the maximum likelihood estimators and on their robust counterparts. The numerical study shows that the Wald tests based on the maximum likelihood estimators or on the unweighted robust ones break down when atypical data arise in the samples, while both the level and power of the Wald-type tests based on redescending weighted M − estimators are stable against the considered contaminations. The analysis of a real data set enables to investigate the p − value sensitivity to the presence of outliers. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
33. Likelihood Ratio Testing under Measurement Errors.
- Author
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Broniatowski, Michel, Jurečková, Jana, and Kalina, Jan
- Subjects
- *
LIKELIHOOD ratio tests , *MEASUREMENT errors , *NULL hypothesis , *PROBABILITY theory , *FALSE positive error - Abstract
We consider the likelihood ratio test of a simple null hypothesis (with density f 0 ) against a simple alternative hypothesis (with density g 0 ) in the situation that observations X i are mismeasured due to the presence of measurement errors. Thus instead of X i for i = 1 , ... , n , we observe Z i = X i + δ V i with unobservable parameter δ and unobservable random variable V i . When we ignore the presence of measurement errors and perform the original test, the probability of type I error becomes different from the nominal value, but the test is still the most powerful among all tests on the modified level. Further, we derive the minimax test of some families of misspecified hypotheses and alternatives. The test exploits the concept of pseudo-capacities elaborated by Huber and Strassen (1973) and Buja (1986). A numerical experiment illustrates the principles and performance of the novel test. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
34. Robust tests in generalized linear models with missing responses
- Author
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Bianco, Ana Maria, Boente, Graciela Lina, and Rodrigues, Isabel
- Subjects
purl.org/becyt/ford/1 [https] ,Influence function ,Generalized linear models ,Ciencias Naturales y Exactas ,Fisher-consistency ,Matemáticas ,Estadística y Probabilidad ,Missing data ,purl.org/becyt/ford/1.1 [https] ,Outliers ,Robust testing - Abstract
In many situations, data follow a generalized linear model in which the mean of the responses is modelled, through a link function, linearly on the covariates. Robust estimators for the regression parameter in order to build test statistics for this parameter, when missing data occur in the responses, are considered. The asymptotic behaviour of the robust estimators for the regression parameter is obtained, under the null hypothesis and under contiguous alternatives. This allows us to derive the asymptotic distribution of the robust Wald-type test statistics constructed from the proposed estimators. The influence function of the test statistics is also studied. A simulation study allows us to compare the behaviour of the classical and robust tests, under different contamination schemes. Applications to real data sets enable to investigate the sensitivity of the p-value to the missing scheme and to the presence of outliers. Fil: Bianco, Ana Maria. Universidad de Buenos Aires. Facultad de Cs.exactas y Naturales. Instituto de Calculo; Argentina; Fil: Boente Boente, Graciela Lina. Consejo Nacional de Invest.cientif.y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Investigaciones Matematicas; Fil: Rodrigues, Isabel. Instituto Superior Tecnico. Department Of Mathematics; Portugal
- Published
- 2013
35. Testing in generalized partially linear models: A robust approach
- Author
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Ricardo Cao, Graciela Boente, Wenceslao González Manteiga, Daniela Rodriguez, and Universidade de Santiago de Compostela. Departamento de Estatística e Investigación Operativa
- Subjects
Statistics and Probability ,Pure mathematics ,Mathematical optimization ,Estadística y Probabilidad ,Matemáticas ,Linear model ,Robust statistics ,Estimator ,Deviance (statistics) ,Rate of convergence ,Nonlinear system ,Kernel weights ,Parametric model ,Generalized partially linear models ,Test statistic ,Robust testing ,Statistics, Probability and Uncertainty ,CIENCIAS NATURALES Y EXACTAS ,Mathematics - Abstract
In this paper, we introduce a family of robust statistics which allow to decide between a parametric model and a semiparametric one. More precisely, under a generalized partially linear model, i.e., when the observations satisfy View the MathML source with View the MathML source and H a known link function, we want to test H0:η(t)=α+γt against H1:η is a nonlinear smooth function. A general approach which includes robust estimators based on a robustified deviance or a robustified quasi-likelihood is considered. The asymptotic behavior of the test statistic under the null hypothesis is obtained. Fil: Boente Boente, Graciela Lina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina Fil: Cao, Ricardo. Universidad da Coruña; España Fil: Gonzalez Manteiga, Wenceslao. Universidad de Santiago de Compostela; España Fil: Rodriguez, Daniela Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
- Published
- 2013
36. Robust tests for Model Selection
- Author
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Lucien Birgé, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, and M. H. Maathuis, Benassù, Serena, and M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, and M. H. Maathuis
- Subjects
Hellinger distance ,model selection ,[MATH.MATH-PR] Mathematics [math]/Probability [math.PR] ,Markov chain ,Markov chains ,[STAT.TH] Statistics [stat]/Statistics Theory [stat.TH] ,Model selection ,010102 general mathematics ,[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] ,01 natural sciences ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,010104 statistics & probability ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,Statistics ,Econometrics ,62G05 ,Robust testing ,62G35 ,0101 mathematics ,[MATH.MATH-ST] Mathematics [math]/Statistics [math.ST] ,Mathematics ,62G10 - Abstract
It was shown almost 40 years ago by Lucien Le Cam that the existence of suitable tests between Hellinger balls in the parameter set led to the construction of some sort of universal estimators for parametric statistical problems with i.i.d. observations. This idea of deriving estimators from families of robust tests was developed and substantially generalized in some of my previous work and more recently extended to Model Selection based estimation. Since the key ingredient for the design of such estimators for a given statistical framework is the construction of the relevant tests for this particular framework, it is essential to explain how to build them for as many different frameworks as possible. The purpose of this paper is to provide improved results about the existence of such tests for the problems of estimation based on independent (not necessarily i.i.d.) observations, estimation of conditional densities and of Markov transitions.
- Published
- 2013
37. A review and some new results on permutation testing for multivariate problems
- Author
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Fortunato Pesarin and Luigi Salmaso
- Subjects
Statistics and Probability ,Multivariate statistics ,Tests for survival functions ,Nonparametric combination ,Nonparametric statistics ,Permutation tests ,Finite sample consistency ,Theoretical Computer Science ,Permutation ,Multi-sided tests ,Robust testing ,Computational Theory and Mathematics ,Sample size determination ,Statistics ,Null distribution ,Statistics, Probability and Uncertainty ,Null hypothesis ,Sufficient statistic ,Mathematics ,Parametric statistics - Abstract
In recent years permutation testing methods have increased both in number of applications and in solving complex multivariate problems. When available permutation tests are essentially of an exact nonparametric nature in a conditional context, where conditioning is on the pooled observed data set which is often a set of sufficient statistics in the null hypothesis. Whereas, the reference null distribution of most parametric tests is only known asymptotically. Thus, for most sample sizes of practical interest, the possible lack of efficiency of permutation solutions may be compensated by the lack of approximation of parametric counterparts. There are many complex multivariate problems, quite common in empirical sciences, which are difficult to solve outside the conditional framework and in particular outside the method of nonparametric combination (NPC) of dependent permutation tests. In this paper we review such a method and its main properties along with some new results in experimental and observational situations (robust testing, multi-sided alternatives and testing for survival functions).
- Published
- 2012
38. Robust GMM analysis of models for the short rate process
- Author
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Elvezio Ronchetti, Fabio Trojani, and Rosario Dell'Aquila
- Subjects
Economics and Econometrics ,Robust model selection ,Model selection ,Monetary policy ,Robust statistics ,One-factor models of interest rates ,Nonlinear system ,Robust estimation ,GMM estimators and tests ,Statistics ,Outlier ,Short rate ,Econometrics ,ddc:330 ,Robust testing ,Cluster analysis ,Finance ,Mathematics ,Generalized method of moments - Abstract
We re-examine the empirical evidence concerning a well-known class of one-factor models for the short rate process (cf. Chan et al. [Journal of Finance 47 (1992) 1209] (CKLS)) and some recent extensions allowing for a nonlinear drift and for changing parameters with a new statistical methodology based on robust statistics, the Robust Generalized Method of Moments (RGMM). We find that standard GMM model selection procedures are highly unstable in these applications. When testing the CKLS models with the RGMM we find that they are all clearly misspecified and we identify a clustering of influential observations in the 1979–1982 subperiod, a time span that is well known to coincide with a temporary change in the monetary policy of the Federal Reserve. This clustering of influential observations does not disappear when we introduce a non-linearity in the drift and allow for a parameter shift during the 1979–1982 period. Moreover, a Cox–Ingersoll–Ross model (selected by the RGMM) might offer a satisfactory data description for the period after 1982, since there only a few isolated outliers are found. Comparable results are obtained for the Euro-mark case.
- Published
- 2003
39. How Large is Average Economic Growth? Evidence from a Robust Method
- Author
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H. Peter Boswijk and Philip Hans Franses
- Subjects
jel:C13 ,jel:C22 ,Growth ,Unit root ,Robust testing ,jel:C15 - Abstract
This paper puts forward a method to estimate average economic growth, andits associated confidence bounds, which does not require a formal decision onpotential unit root properties. The method is based on the analysis of eitherdifference-stationary or trend-stationary time series models, implementing the robustbootstrapping procedure advocated in Romano and Wolf (2001). Simulation evidence indicatesthe practical relevance of the method. It is illustrated on quarterly post-war USindustrial production.
- Published
- 2002
40. How Large is Average Economic Growth? Evidence from a Robust Method
- Author
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Boswijk, H. Peter and Franses, Philip Hans
- Subjects
Unit Root Test ,Wirtschaftswachstum ,Unit root ,Robustes Verfahren ,ddc:330 ,C13 ,C15 ,Growth ,Robust testing ,C22 - Abstract
This paper puts forward a method to estimate average economic growth, andits associated confidence bounds, which does not require a formal decision onpotential unit root properties. The method is based on the analysis of eitherdifference-stationary or trend-stationary time series models, implementing the robustbootstrapping procedure advocated in Romano and Wolf (2001). Simulation evidence indicatesthe practical relevance of the method. It is illustrated on quarterly post-war USindustrial production.
- Published
- 2002
41. Short Patches of Outliers, ARCH and Volatility Modeling
- Author
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Philip Hans Franses, Dick van Dijk, and André Lucas
- Subjects
Generalized AutoRegressive Conditional Heteroskedasticity ,Lagrange Multiplier test ,Outliers ,Robust testing ,Exchange rates ,Stock market indices - Abstract
In this paper we test for (Generalized) AutoRegressive Conditional Heteroskedasticity [(G)ARCH] in daily data on 22 exchange rates and 13 stock market indices using the standard Lagrange Multiplier [LM] test for GARCH and a LM test that is resistant to patches of additive outliers. The data span two samples of 5 years ranging from 1986 to 1995. Using asymptotic arguments and Monte Carlo simulations, in which we evaluate our empirical method, we show that patches of outliers can have significant effects on test outcomes. Our main empirical result is that we find spurious GARCH in about 40% of the cases, while in many other cases we find evidence of GARCH even though such sequences of extraordinary observations seem to be present.
- Published
- 1998
42. Short Patches of Outliers, ARCH and Volatility Modeling
- Author
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Franses, P. H., Dijk, D., Andre Lucas, and Econometrics and Data Science
- Subjects
Welt ,Generalized AutoRegressive Conditional Heteroskedasticity ,Exchange rates ,ddc:330 ,Lagrange Multiplier test ,Outliers ,Schätztheorie ,Robust testing ,Stock market indices ,Börsenkurs ,Wechselkurs ,Theorie - Abstract
In this paper we test for (Generalized) AutoRegressive Conditional Heteroskedasticity [(G)ARCH] in daily data on 22 exchange rates and 13 stock market indices using the standard Lagrange Multiplier [LM] test for GARCH and a LM test that is resistant to patches of additive outliers. The data span two samples of 5 years ranging from 1986 to 1995. Using asymptotic arguments and Monte Carlo simulations, in which we evaluate our empirical method, we show that patches of outliers can have significant effects on test outcomes. Our main empirical result is that we find spurious GARCH in about 40% of the cases, while in many other cases we find evidence of GARCH even though such sequences of extraordinary observations seem to be present.
- Published
- 1998
43. A tail area influence function and its application to testing
- Author
-
C.A. Fiel and Elvezio Ronchetti
- Subjects
Statistics and Probability ,robust testing ,Maximum level ,influence function ,small sample asymptotios ,level and power ,Small sample ,Sample (statistics) ,Power (physics) ,Modeling and Simulation ,Statistics ,ddc:330 ,Gross error model ,Influence function ,Mathematics - Abstract
A tail area influence function is introduced and, for tests Tn determined as solutions of small sample asymptotics are used to compute this influence function. Its relationship to other influence functions for testing is examined and it is shown to be a finite sample refinement of the level and power influence function. Approximations for the maximum level and minimum power for a gross error model are computed.
- Published
- 1985
44. Robust tests based on dual divergence estimators and saddlepoint approximations
- Author
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Samuela Leoni-Aubin, Aida Toma, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Gheorghe Mihoc -Caius Iacob, and Institute of Mathematical Statistics and Applied Mathematics, Bucharest
- Subjects
Statistics and Probability ,Approximation theory ,Numerical Analysis ,010102 general mathematics ,Estimator ,[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] ,Asymptotic theory (statistics) ,M-estimators ,01 natural sciences ,010104 statistics & probability ,Sample size determination ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,Divergences ,Parametric model ,Calculus ,Applied mathematics ,p-value ,Robust testing ,0101 mathematics ,Statistics, Probability and Uncertainty ,Divergence (statistics) ,Saddlepoint approximations ,ComputingMilieux_MISCELLANEOUS ,Mathematics ,Statistical hypothesis testing - Abstract
This paper is devoted to robust hypothesis testing based on saddlepoint approximations in the framework of general parametric models. As is known, two main problems can arise when using classical tests. First, the models are approximations of reality and slight deviations from them can lead to unreliable results when using classical tests based on these models. Then, even if a model is correctly chosen, the classical tests are based on first order asymptotic theory. This can lead to inaccurate p-values when the sample size is moderate or small. To overcome these problems, robust tests based on dual divergence estimators and saddlepoint approximations, with good performances in small samples, are proposed.
- Full Text
- View/download PDF
45. Binary Experiments, Minimax Tests and 2-Alternating Capacities
- Author
-
Tadeusz Bednarski
- Subjects
Statistics and Probability ,Mathematical optimization ,Lemma (mathematics) ,Binary number ,binary experiments ,Characterization (mathematics) ,Minimax ,Set (abstract data type) ,Strassen algorithm ,minimax testing ,Applied mathematics ,Robust testing ,62G35 ,Statistics, Probability and Uncertainty ,Mathematics ,Probability measure ,capacities ,62B15 - Abstract
The concept of Choquet's 2-alternating capacity is explored from the viewpoint of Le Cam's experiment theory. It is shown that there always exists a least informative binary experiment for two sets of probability measures generated by 2-alternating capacities. This result easily implies the Neyman-Pearson lemma for capacities. Moreover, its proof gives a new method of construction of minimax tests for problems in which hypotheses are generated by 2-alternating capacities. It is also proved that the existence of least informative binary experiments is sufficient for a set of probability measures to be generated by a 2-alternating capacity. This gives a new characterization of 2-alternating capacities, closely related to that of Huber and Strassen.
- Published
- 1982
46. Binary Experiments, Minimax Tests and 2-Alternating Capacities
- Author
-
Bednarski, Tadeusz
- Published
- 1982
47. Robust C(α)-Type Tests for Linear Models
- Author
-
Ronchetti, Elvezio
- Published
- 1987
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