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The paper deals with the classical two-sample problem for the combined location-scale and Lehmann alternatives, known as the versatile alternative. Recently, a combination of the square of the standardized Wilcoxon, the standardized Ansari–Bradley and the standardized Anti-Savage statistics based on the Euclidean distance has been proposed. The Anti-Savage test is the locally most powerful rank test for the right-skewed Gumbel distribution. Furthermore, the Savage test is the locally most powerful linear rank test for the left-skewed Gumbel distribution. Then, a test statistic combining the Wilcoxon, the Ansari–Bradley, and Savage statistics is proposed. The limiting distribution of the proposed statistic is derived under the null and the alternative hypotheses. In addition, the asymptotic power of the suggested statistic is investigated. Moreover, an adaptive test is proposed based on a selection rule. We compare the power performance against various fixed alternatives using Monte Carlo. The proposed test statistic displays outstanding performance in certain situations. An illustration of the proposed test statistic is presented to explain a biomedical experiment. Finally, we offer some concluding remarks. [ABSTRACT FROM AUTHOR]

This study examines interpoint distance-based tests for random elements from probability distributions in infinite-dimensional space. Some asymptotic properties such as the limiting distributions and the asymptotic power of the Biswas–Ghosh type test (Biswas and Ghosh in J Multivar Anal 123: 160–171, 2014) are presented using the theory of U-statistic. In addition, the p-value approximation based on the jackknife variance estimators and the Welch–Satterthwaite equation is proposed. Simulation studies are conducted to evaluate the performance of the proposed test statistics in functional data analysis. The proposed tests are shown to have better power than the existing method for functional data in some situations. [ABSTRACT FROM AUTHOR]

This study proposes two modified Anderson-Darling test statistics that emphasize the upper or lower tails of distribution. Under the finite sample sizes, various models are used to estimate the upper tail percentage points of the proposed test statistic. The limiting distribution of the proposed test statistics is derived with a sum of infinite series. The polynomial approximation, the method of Durbin and Knott and the normal and non normal saddlepoint approximations are used to approximate the limiting distribution of the suggested test statistics. Simulations are used to investigate the accuracy of various approximations. The asymptotic power of the proposed statistics is obtained to compare with various statistics. The proposed test statistics are illustrated by the analysis of real data. [ABSTRACT FROM AUTHOR]

The Hawkes process is a popular point process model for events that exhibit a local clustering behaviour. Chen and Hall studied the asymptotic inference theory for a nonstationary Hawkes process where the baseline intensity is proportional to some time-varying function with the proportionality constant n tending to infinity. However, they assumed the excitation kernel to be independent of n , and therefore, as n increases, the waiting times from a baseline event to its excited events are of order O P (1) while the waiting times between baseline events is O P (1 / n) , suggesting the excitation effect is not local anymore, which defeats the purpose of choosing the exponential excitation kernel in the first place. To avoid this issue, we study the model in a more realistic setting where the excitation kernel also depends on the limit index n , so that the waiting times to excited events are of the same order of magnitude as those between baseline events. We establish consistency and asymptotic normality of the Maximum Likelihood Estimator (MLE). We also propose a score test to assess the constancy of the baseline intensity function and derive the asymptotic properties of the test. We apply the MLE and the score test to ultra-high frequency financial data as well as evaluating their finite sample performance via simulation experiments. • An alternative scenario of asymptotics to Chen and Hall [2013] is considered. • An approximation procedure is formulated to study the model's asymptotics. • A MLE program is realised, with consistency and asymptotic normality. • Asymptotic distribution of the score test statistic is identified. • Power of the score test was investigated. [ABSTRACT FROM AUTHOR]

Several statistical tests have been proposed in the literature to assess the difference between two scale parameters in paired data. If the location parameters of each sample are different, many of these test statistics are adjusted using the estimated location parameters. Then, the performance of the test statistics depends on the selection of the location estimators. In this study, the asymptotically distribution-free test based on the U-statistic, which does not depend on two location parameters, is constructed. The asymptotic normality and the asymptotic power of the proposed test are examined. Furthermore, the proposed test is compared with the existing tests in terms of Pitman's asymptotic relative efficiency. To improve the Type I error rate in the small sample size, the robust test procedure based on the percentile bootstrap is also proposed. Our simulation studies show that the Type I error rate of the proposed test is more controlled and robust than existing tests in many situations. Further, the empirical power of the proposed test is shown to be high for heavy-tailed or asymmetric distributions. [ABSTRACT FROM AUTHOR]

Summary: Identification of peer effects is complicated by the fact that the individuals under study may select their peers. Random assignment to peer groups has proven useful to sidestep such a concern. In the absence of a formal randomization mechanism, it needs to be argued that assignment is "as good as" random. This paper introduces a simple yet powerful test to do so. We provide theoretical results for this test. As a by‐product, we equally obtain such results for an approach popularized by Guryan et al. (2009). These results help to explain why this approach suffers from low power, as has been observed elsewhere. [ABSTRACT FROM AUTHOR]

We consider the problem of designing experiments to detect the presence of a specified heteroscedastity in Gaussian regression models. We study the relationship of the D s - and KL-criteria with the noncentrality parameter of the asymptotic chi-squared distribution of a likelihood-based test, for local alternatives. We found that, when the heteroscedastity depends on one parameter, the two criteria coincide asymptotically and that the D1-criterion is proportional to the noncentrality parameter. Differently, when it depends on several parameters, the KL-optimum design converges to the design that maximizes the noncentrality parameter. Our theoretical findings are confirmed through a simulation study. [ABSTRACT FROM AUTHOR]

The two one-sided t-tests (TOST) method is the most popular statistical equivalence test with many areas of application, i.e., in the pharmaceutical industry. Proper sample size calculation is needed in order to show equivalence with a certain power. Here, the crucial problem of choosing a suitable mean-difference in TOST sample size calculations is addressed. As an alternative concept, it is assumed that the mean-difference follows an a-priori distribution. Special interest is given to the uniform and some centered triangle a-priori distributions. Using a newly developed asymptotical theory a helpful analogy principle is found: every a-priori distribution corresponds to a point mean-difference, which we call its Schuirmann-constant. This constant does not depend on the standard deviation and aims to support the investigator in finding a well-considered mean-difference for proper sample size calculations in complex data situations. In addition to the proposed concept, we demonstrate that well-known sample size approximation formulas in the literature are in fact biased and state their unbiased corrections as well. Moreover, an R package is provided for a right away application of our newly developed concepts. [ABSTRACT FROM AUTHOR]

One-sample testing problem is one of the most important topics in statistics. The sign and Wilcoxon tests are commonly used for testing the location parameter. An extension of the sign and Wilcoxon signed-rank tests has been proposed. However, when the sample size increases, the exact critical value of the statistic becomes difficult to determine. Therefore, in this study, we used a saddlepoint approximation with continuity correction to approximate the distribution of the statistic. Our numerical results illustrate that the saddlepoint approximation to the statistic is more suitable than the normal approximation. We also derived the asymptotic power under the alternative hypothesis and investigated the unbiasedness and biasedness of the test conducted in this study. [ABSTRACT FROM AUTHOR]

Summary: Various non‐parametric goodness of fit tests have already been investigated in the literature. However, those tests are rarely used in the case of missing observations. We here study the goodness of fit test for missing data based on Lp distances along with Kolmogorov–Smirnov and Cramer–von‐Mises distances when missingness occurs at random. The asymptotic distributions of the proposed test statistics have been derived under contiguous alternatives that enable us to investigate the asymptotic local power of the tests. We also study the performance of the tests for finite samples using simulation, and the tests perform well for those cases. The usefulness of the tests is illustrated on three real data sets. Non‐parametric goodness of fit tests which are based on Lp distances including the well known Kolmogorov‐Smirnov and Cramer‐von‐Mises distances are studied under missing data when the missing mechanism is random (MAR). The asymptotic distributions of the proposed test statistics have been derived under contiguous alternatives. Then we also investigate the asymptotic local power of the tests. [ABSTRACT FROM AUTHOR]

In this article, we develop a test for multivariate location parameter in elliptical model based on the forward search estimator for a specified scatter matrix. Here, we study the asymptotic power of the test under contiguous alternatives based on the asymptotic distribution of the test statistics under such alternatives. Moreover, the performances of the test have been carried out for different simulated data and real data, and compared the performances with more classical ones. [ABSTRACT FROM AUTHOR]

For the multi-sample equal covariance function (ECF) testing problem, Zhang (Analysis of variance for functional data, CRC Press, Boca Raton, 2013) proposed an L 2 -norm-based test. However, its asymptotic power and finite sample performance have not been studied. In this paper, its asymptotic power is investigated under some mild conditions. It is shown that the L 2 -norm-based test is root-n consistent. In addition, intensive simulation studies are conducted to evaluate its finite sample performance against several existing competitors. In particular, they demonstrate that in terms of size control and power, the L 2 -norm-based test outperforms the dimension-reduction-based tests proposed by Panaretos et al. (J Am Stat Assoc 105(490):670–682, 2010) and Fremdt et al. (Scand J Stat 40(1):138–152, 2013), respectively, when functional data are less correlated or when the covariance function differences of functional data contain mainly high-frequency signals. Two real data applications are presented to illustrate the L 2 -norm-based test. [ABSTRACT FROM AUTHOR]

We propose a class of ratio tests that is applicable whenever a cumulation (of transformed) data is asymptotically normal upon appropriate normalization. The Karhunen–Loève theorem is employed to compute weighted averages. The test statistics are ratios of quadratic forms of these averages and hence scale-invariant, also called self-normalizing: The scaling parameter cancels asymptotically. Limiting distributions are obtained. Critical values and asymptotic local power functions can be calculated by standard numerical means. The ratio tests are directed against local alternatives and turn out to be almost as powerful as optimal competitors, without being plagued by nuisance parameters at the same time. Also in finite samples they perform well relative to self-normalizing competitors. [ABSTRACT FROM AUTHOR]

In this paper Pitman's asymptotic efficiency (AE) as well as Kallenberg's intermediate AE of the goodness-of-fit tests based on higher-order non-overlapping spacings is considered. We study log statistic as well as entropy type statistic based on k-spacings when k may tend to infinity as n approaches infinity. It certainly compliments the available results for fixed k and provides more general result. We show that both types of statistics based on higher ordered spacings have higher efficiencies in Pitman's sense compared to their counterparts based on simple spacings. It is also shown that the Kallenberg's intermediate AE of such test coincides with its Pitman's AE, the power of the tests are also discussed. [ABSTRACT FROM AUTHOR]

Abstract: Consider a non‐parametric regression model Y=m(X)+ϵ, where m is an unknown regression function, Y is a real‐valued response variable, X is a real covariate, and ϵ is the error term. In this article, we extend the usual tests for homoscedasticity by developing consistent tests for independence between X and ϵ. Further, we investigate the local power of the proposed tests using Le Cam's contiguous alternatives. An asymptotic power study under local alternatives along with extensive finite sample simulation study shows that the performance of the new tests is competitive with existing ones. Furthermore, the practicality of the new tests is shown using two real data sets. [ABSTRACT FROM AUTHOR]

The paper describes non-parametric approach for analysis of a three-period, two-treatment, four-sequence crossover design in which test procedure for interchangeability of the treatment effects is obtained. The proposed procedure is based on a non-parametric model, which incorporates, along with the direct treatment effects and the usual carryover effects, the long-term carryover effects. Relevant competitors are obtained. Related asymptotic results are given. By performing simulation study, we compared the procedures with respect to type I error rate and power. Furthermore, confidence intervals for treatment differences are studied. The procedures are illustrated with a data study. [ABSTRACT FROM AUTHOR]

This paper studies the asymptotic power for the sphericity test in a fixed effect panel data model proposed by Baltagi et al. (2011), (JBFK). This is done under the alternative hypotheses of weak and strong factors. By weak factors, we mean that the Euclidean norm of the vector of the factor loadings isO(1). By strong factors, we mean that the Euclidean norm of the vector of factor loadings is, wherenis the number of individuals in the panel. To derive the limiting distribution ofJBFKunder the alternative, we first derive the limiting distribution of its raw data counterpart. Our results show that, when the factor is strong, the test statistic diverges in probability to infinity as fast asOp(nT). However, when the factor is weak, its limiting distribution is a rightward mean shift of the limit distribution under the null. Second, we derive the asymptotic behavior of the difference betweenJBFKand its raw data counterpart. Our results show that when the factor is strong, this difference is as large asOp(n). In contrast, when the factor is weak, this difference converges in probability to a constant. Taken together, these results imply that when the factor is strong,JBFKis consistent, but when the factor is weak,JBFKis inconsistent even though its asymptotic power is nontrivial. [ABSTRACT FROM AUTHOR]

We consider the problem of detecting the presence of a submatrix with larger-than-usual values in a large data matrix. This problem was considered in Butucea and Ingster (2013) under a one-parameter exponential family, and one of the procedures they analyzed is the scan test. Taking a nonparametric stance, we show that a calibration by permutation leads to the same (first-order) asymptotic performance. This is true for the two types of permutations we consider. We also study the corresponding rank-based variants and quantify precisely the loss in asymptotic power. [ABSTRACT FROM AUTHOR]

We discuss a one-sample location test that can be used when the dimension and the sample size are large. It is well-known that the power of Hotelling’s test decreases when the dimension is close to the sample size. To address this loss of power, some non exact approaches were proposed, e.g., Dempster (1958, 1960), Bai and Saranadasa (1996), and Srivastava and Du (2008). In this article, we focus on Hotelling’s test and Dempster’s test. The comparative merits and demerits of these two tests vary according to the local parameters. In particular, we consider the situation where it is difficult to determine which test should be used, that is, where the two tests are asymptotically equivalent in terms of local power. We propose a new statistic based on the weighted averaging of Hotelling’sT2-statistic and Dempster’s statistic that can be applied in such a situation. Our weight is determined on the basis of the maximum local asymptotic power on a restricted parameter space that induces local asymptotic equivalence between Hotelling’s test and Dempster’s test. Numerical results show that our test is more stable than Hotelling’sT2-statistic and Dempster’s statistic in most parameter settings. [ABSTRACT FROM PUBLISHER]

A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large dimensional, non-parametric double-cone alternative. For example, the test against a constant function uses the alternative of increasing or decreasing regression functions, and the test against a linear function uses the convex or concave alternative. The test proposed is exact and unbiased and the critical value is easily computed. The power of the test increases to 1 as the sample size increases, under very mild assumptions-even when the alternative is misspecified, i.e. the power of the test converges to 1 for any true regression function that deviates (in a non-degenerate way) from the parametric null hypothesis. We also formulate tests for the linear versus partial linear model and consider the special case of the additive model. Simulations show that our procedure behaves well consistently when compared with other methods. Although the alternative fit is non-parametric, no tuning parameters are involved. Supplementary materials with proofs and technical details are available on line. [ABSTRACT FROM AUTHOR]

We examine the behaviour of OLS-demeaned/detrended and GLS-demeaned/detrended unit root tests that employ stationary covariates, as proposed by Hansen (1995, 'Rethinking the Univariate Approach to Unit Root Testing.' Econometric Theory 11:1148-71) and Elliott and Jansson (2003, 'Testing for Unit Roots with Stationary Covariates.' Journal of Econometrics 115:75-89), respectively, in situations where the magnitude of the initial condition of the time series under consideration may be non-negligible. We show that the asymptotic power of such tests is very sensitive to the initial condition; OLS- and GLS-based tests achieve relatively high power for large and small magnitudes of the initial condition, respectively. Combining information from both types of test via a simple union of rejections strategy is shown to effectively capture the higher power available across all initial condition magnitudes. [ABSTRACT FROM AUTHOR]

We introduce a class of nonparametric two-sample tests based on a new partially sequential sampling scheme. Existing partially sequential procedures based on inverse sampling schemes, pioneered by Wolfe (1977) and Orban and Wolfe (1980), are updated in the light of random sequential sampling techniques, proposed by Mukhopadhyay and de Silva (2008). In a quality control setup, the present procedure can be looked upon as a Phase II on-line monitoring with rational subgroups of variable sizes where standards are unknown. We consider a training sample of prefixed sizemas Phase I observations and adopt a random sequential sampling in Phase II. We discuss statistical methodologies in detail and provide some asymptotic results. Numerical results based on Monte Carlo are presented to justify asymptotic theory. We computationally investigate the power performances of the proposed test against some fixed alternative. We illustrate our procedure with real data related to water samples for monitoring arsenic contamination. Some concluding remarks along with possible future research problems are offered [ABSTRACT FROM AUTHOR]

In a two-sample testing problem, sometimes one of the sample observations are difficult and/or costlier to collect compared to the other one. Also, it may be the situation that sample observations from one of the populations have been previously collected and for operational advantages we do not wish to collect any more observations from the second population that are necessary for reaching a decision. Partially sequential technique is found to be very useful in such situations. The technique gained its popularity in statistics literature due to its very nature of capitalizing the best aspects of both fixed and sequential procedures. The literature is enriched with various types of partially sequential techniques useable under different types of data set-up. Nonetheless, there is no mention of multivariate data framework in this context, although very common in practice. The present paper aims at developing a class of partially sequential nonparametric test procedures for two-sample multivariate continuous data. For this we suggest a suitable stopping rule adopting inverse sampling technique and propose a class of test statistics based on the samples drawn using the suggested sampling scheme. Various asymptotic properties of the proposed tests are explored. An extensive simulation study is also performed to study the asymptotic performance of the tests. Finally the benefit of the proposed test procedure is demonstrated with an application to a real-life data on liver disease. [ABSTRACT FROM AUTHOR]

The paper describes a nonparametric model for the analysis of the two-treatment, two-period, four-sequence crossover design. Tests for the equality of treatment effects and for the absence of carryover effects are provided. Some relevant asymptotic results of the proposed tests are obtained and compared with the existing nonparametric and parametric competitors via simulation. It is shown that the proposed tests are comparable to or better than the competitors in terms of type I error and power. [ABSTRACT FROM AUTHOR]

Recently, Mukherjee and Bandyopadhyay (J Stat Plan Inference, , doi:) introduced some partially sequential tests for detecting liner trend among the incoming series of observations when a training sample is available a-priori. Their work is very useful in econometric or environmental monitoring under certain situations. The present work is intended for generalization of their tests for any monotone trend. We develop two nonparametric tests for the identity of some unknown univariate continuous distribution functions against monotone or unidirectional trend in location. One of these two tests is based on usual ranks and the other is based on sequential ranks. These are typical nonparametric tests for monitoring structural changes. Performance of the two tests are compared using asymptotic studies as well as through some numerical results based on Monte-Carlo simulations. An illustration is offered using a real data on monthly production of certain beverage. [ABSTRACT FROM AUTHOR]

In this paper, we propose an instrumental variable approach to constructing confidence sets (CS's) for the true parameter in models defined by conditional moment inequalities/equalities. We show that by properly choosing instrument functions, one can transform conditional moment inequalities/equalities into unconditional ones without losing identification power. Based on the unconditional moment inequalities/equalities, we construct CS's by inverting Cramer-von Mises-type or Kolmogorov-Smirnov-type tests. Critical values are obtained using generalized moment selection (GMS) procedures. We show that the proposed CS's have correct uniform asymptotic coverage probabilities. New methods are required to establish these results because an infinite-dimensional nuisance parameter affects the asymptotic distributions. We show that the tests considered are consistent against all fixed alternatives and typically have power against n~l/2-local alternatives to some, but not all, sequences of distributions in the null hypothesis. Monte Carlo simulations for five different models show that the methods perform well in finite samples. [ABSTRACT FROM AUTHOR]

This paper is concerned with tests and confidence intervals for parameters that are not necessarily point identified and are defined by moment inequalities. In the literature, different test statistics, critical-value methods, and implementation methods (i.e., the asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare these methods. We provide a recommended test statistic, moment selection critical value, and implementation method. We provide data-dependent procedures for choosing the key moment selection tuning parameter κ and a size-correction factor ɳ [ABSTRACT FROM AUTHOR]