32 results on '"62G32"'
Search Results
2. Marshall–Olkin type copulas generated by a global shock.
- Author
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Durante, Fabrizio, Girard, Stéphane, and Mazo, Gildas
- Subjects
- *
COPULA functions , *MATHEMATICAL transformations , *UNIVARIATE analysis , *MATHEMATICAL functions , *SEMIGROUPS (Algebra) , *SYSTEMS theory , *MATHEMATICAL models - Abstract
A way to transform a given copula by means of a univariate function is presented. The resulting copula can be interpreted as the result of a global shock affecting all the components of a system modeled by the original copula. The properties of this copula transformation from the perspective of semi-group action are presented, together with some investigations about the related tail behavior. Finally, the whole methodology is applied to model risk assessment. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
3. Kernel estimation of the tail index of a right-truncated Pareto-type distribution.
- Author
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Benchaira, Souad, Meraghni, Djamel, and Necir, Abdelhakim
- Subjects
- *
KERNEL functions , *PARETO distribution , *ESTIMATION theory , *SIMULATION methods & models , *EXISTENCE theorems - Abstract
An asymptotically normal kernel estimator for the positive tail index of right-truncated data is introduced. A simulation study shows that the proposed estimator performs much better than the existing ones in terms of bias. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
4. A Lynden-Bell integral estimator for extremes of randomly truncated data.
- Author
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Worms, J. and Worms, R.
- Subjects
- *
INTEGRALS , *ESTIMATION theory , *EXTREME value theory , *ASYMPTOTIC expansions , *MATHEMATICAL forms - Abstract
In the framework of heavy-tailed randomly truncated data, a new estimator is proposed for the extreme value index in a natural Lynden-Bell integral form. Extreme quantiles are also estimated, and the asymptotic normality is established under mild assumptions. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
5. A general study of extremes of stationary tessellations with examples.
- Author
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Chenavier, Nicolas
- Subjects
- *
TESSELLATIONS (Mathematics) , *MATHEMATICAL proofs , *MATHEMATICAL bounds , *BOREL subsets , *CONVEX bodies , *STATISTICAL association , *POISSON'S equation - Abstract
Abstract: Let be a random tessellation in , , observed in a bounded Borel subset and be a measurable function defined on the set of convex bodies. A point , called the nucleus of , is associated with each cell of . Applying to all the cells of , we investigate the order statistics of over all cells with nucleus in when goes to infinity. Under a strong mixing property and a local condition on and , we show a general theorem which reduces the study of the order statistics to the random variable , where is the typical cell of . The proof is deduced from a Poisson approximation on a dependency graph via the Chen–Stein method. We obtain that the point process , where and are two suitable functions depending on , converges to a non-homogeneous Poisson point process. Several applications of the general theorem are derived in the particular setting of Poisson–Voronoi and Poisson–Delaunay tessellations and for different functions such as the inradius, the circumradius, the area, the volume of the Voronoi flower and the distance to the farthest neighbor. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
6. Ensemble statistical post-processing of the National Air Quality Forecast Capability: Enhancing ozone forecasts in Baltimore, Maryland.
- Author
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Garner, Gregory G. and Thompson, Anne M.
- Subjects
- *
AIR quality research , *EMISSION standards , *AIR pollution , *OZONE , *SURFACE analysis - Abstract
Abstract: An ensemble statistical post-processor (ESP) is developed for the National Air Quality Forecast Capability (NAQFC) to address the unique challenges of forecasting surface ozone in Baltimore, MD. Air quality and meteorological data were collected from the eight monitors that constitute the Baltimore forecast region. These data were used to build the ESP using a moving-block bootstrap, regression tree models, and extreme-value theory. The ESP was evaluated using a 10-fold cross-validation to avoid evaluation with the same data used in the development process. Results indicate that the ESP is conditionally biased, likely due to slight overfitting while training the regression tree models. When viewed from the perspective of a decision-maker, the ESP provides a wealth of additional information previously not available through the NAQFC alone. The user is provided the freedom to tailor the forecast to the decision at hand by using decision-specific probability thresholds that define a forecast for an ozone exceedance. Taking advantage of the ESP, the user not only receives an increase in value over the NAQFC, but also receives value for costly decisions that the NAQFC couldn't provide alone. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
7. Analysis of high level ozone concentrations using nonparametric methods
- Author
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Quintela-del-Río, Alejandro and Francisco-Fernández, Mario
- Subjects
- *
ATMOSPHERIC ozone , *AIR pollution , *EMISSION control , *AIR quality , *ESTIMATION theory , *EXTREME value theory , *NITROGEN dioxide - Abstract
Abstract: Controlling emissions of air pollutants and establishing air quality objectives to improve and protect ambient air quality are very important tasks of Governments. Ozone (O3), one of those pollutants of concern, is not emitted directly into the atmosphere, but is a secondary pollutant produced by reaction between nitrogen dioxide (NO2), hydrocarbons and sunlight. High levels of ozone can produce harmful effects on human health and the environment in general. Therefore, the study of extreme values of ozone represents an important topic of research in environmental problems. Classical extreme value theory has been usually used in air-pollution studies. It consists of fitting a parametric generalized extreme value (GEV) distribution to a data set of extreme values and using the estimated distribution to compute quantities like the probability of exceedance, the quantiles, the return levels or the mean return periods. In this paper, we propose nonparametric methods to estimate those quantities. Additionally, nonparametric estimators of the trends of very high values of ozone are proposed. The nonparametric estimators are applied to real samples of maximum ozone values obtained from several monitoring stations belonging to the Automatic Urban and Rural Network (AURN) from the UK. Results show that nonparametric estimators work satisfactorily, generally outperforming the behaviour of classical parametric estimators. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
8. Nonparametric functional data estimation applied to ozone data: Prediction and extreme value analysis
- Author
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Quintela-del-Rı´o, Alejandro and Francisco-Fernández, Mario
- Subjects
- *
EXTREME value theory , *AIR pollution , *DATA analysis , *METHODOLOGY , *OZONE layer , *TIME series analysis - Abstract
Abstract: The study of extreme values and prediction of ozone data is an important topic of research when dealing with environmental problems. Classical extreme value theory is usually used in air-pollution studies. It consists in fitting a parametric generalised extreme value (GEV) distribution to a data set of extreme values, and using the estimated distribution to compute return levels and other quantities of interest. Here, we propose to estimate these values using nonparametric functional data methods. Functional data analysis is a relatively new statistical methodology that generally deals with data consisting of curves or multi-dimensional variables. In this paper, we use this technique, jointly with nonparametric curve estimation, to provide alternatives to the usual parametric statistical tools. The nonparametric estimators are applied to real samples of maximum ozone values obtained from several monitoring stations belonging to the Automatic Urban and Rural Network (AURN) in the UK. The results show that nonparametric estimators work satisfactorily, outperforming the behaviour of classical parametric estimators. Functional data analysis is also used to predict stratospheric ozone concentrations. We show an application, using the data set of mean monthly ozone concentrations in Arosa, Switzerland, and the results are compared with those obtained by classical time series (ARIMA) analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
9. Goodness-of-fit testing for Weibull-type behavior
- Author
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Goegebeur, Yuri and Guillou, Armelle
- Subjects
- *
GOODNESS-of-fit tests , *WEIBULL distribution , *DATA analysis , *INFERENCE (Logic) , *PARAMETER estimation , *ASYMPTOTIC expansions , *SIMULATION methods & models - Abstract
Abstract: In the process of analyzing data, testing the fit of a model under consideration is a prerequisite for performing inference about the model parameters. In this paper we examine the goodness-of-fit testing problem for assessing whether a sample is consistent with the Weibull-type model. Inspired by the Jackson and the Lewis test statistics, originally proposed as goodness-of-fit tests for the exponential distribution, we introduce two new statistics for testing Weibull-type behavior, and study their asymptotic properties. Moreover, given that the statistics are ratios of estimators for the Weibull-tail coefficient, we obtain new estimators for the latter, and establish their consistency and asymptotic normality. The small sample behavior of our statistics and estimators is evaluated on the basis of a simulation study. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
- View/download PDF
10. Weak convergence of the tail empirical process for dependent sequences
- Author
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Rootzén, Holger
- Subjects
- *
STOCHASTIC convergence , *STATIONARY sequences (Mathematics) , *MATHEMATICAL sequences , *STATIONARY processes - Abstract
Abstract: This paper proves weak convergence in of the tail empirical process–the renormalized extreme tail of the empirical process–for a large class of stationary sequences. The conditions needed for convergence are (i) moment restrictions on the amount of clustering of extremes, (ii) restrictions on long range dependence (absolute regularity or strong mixing), and (iii) convergence of the covariance function. We further show how the limit process is changed if exceedances of a nonrandom level are replaced by exceedances of a high quantile of the observations. Weak convergence of the tail empirical process is one key to asymptotics for extreme value statistics and its wide range of applications, from geoscience to finance. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
11. Goodness-of-fit tests for a heavy tailed distribution
- Author
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Koning, Alex J. and Peng, Liang
- Subjects
- *
MATHEMATICS , *DISTRIBUTION (Probability theory) , *PROBABILITY theory , *MATHEMATICAL statistics - Abstract
Abstract: We study the Kolmogorov–Smirnov test, Berk–Jones test, score test and their integrated versions in the context of testing the goodness-of-fit of a heavy tailed distribution function. A comparison of these tests is conducted via Bahadur efficiency and simulations. In the simulations, the score test and the integrated score test show the best performance. Although the Berk–Jones test is more powerful than the Kolmogorov–Smirnov test, this does not hold true for their integrated versions; this differs from results in Einmahl et al. [2003. Empirical likelihood based hypothesis testing. Bernoulli 9(2), 267–290], which shows the difference of Berk–Jones test in testing distributions and tails. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
12. Bayesian mixture modeling for spatial Poisson process intensities, with applications to extreme value analysis
- Author
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Kottas, Athanasios and Sansó, Bruno
- Subjects
- *
POISSON processes , *DENSITY functionals , *NONPARAMETRIC statistics , *BOUNDARY value problems , *UNIFORM distribution (Probability theory) - Abstract
We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial nonhomogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the space where the process is defined. The method is based on modeling a density function, defined on this bounded region, that is directly related with the intensity function of the Poisson process. We develop a flexible nonparametric mixture model for this density using a bivariate Beta distribution for the mixture kernel and a Dirichlet process prior for the mixing distribution. Using posterior simulation methods, we obtain full inference for the intensity function and any other functional of the process that might be of interest. We discuss applications to problems where inference for clustering in the spatial point pattern is of interest. Moreover, we consider applications of the methodology to extreme value analysis problems. We illustrate the modeling approach with three previously published data sets. Two of the data sets are from forestry and consist of locations of trees. The third data set consists of extremes from the Dow Jones index over a period of 1303 days. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
13. Sharp bounds on expectations of second record increments from decreasing density families
- Author
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Raqab, Mohammad Z.
- Subjects
- *
MATHEMATICAL statistics , *MULTIVARIATE analysis , *DISTRIBUTION (Probability theory) , *MATHEMATICAL models - Abstract
Abstract: In this paper, we derive sharp upper bounds on expectations of non-adjacent increments of second record statistics based on independent samples from decreasing density families of distributions. We also determine the distributions for which the bounds are attained. These bounds are based on a projection method. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
14. Approximations to the tail empirical distribution function with application to testing extreme value conditions
- Author
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Drees, Holger, de Haan, Laurens, and Li, Deyuan
- Subjects
- *
DISTRIBUTION (Probability theory) , *REGRESSION analysis , *ANALYSIS of variance , *MATHEMATICAL statistics - Abstract
Abstract: Weighted approximations to the tail of the distribution function and its empirical counterpart are derived which are suitable for applications in extreme value statistics. The approximation of the tail empirical distribution function is then used to develop an Anderson–Darling type test of the null hypothesis that the distribution function belongs to the domain of attraction of an extreme value distribution. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
15. The contribution of the maximum to the sum of excesses for testing max-domains of attraction
- Author
-
Neves, Cláudia, Picek, Jan, and Fraga Alves, M.I.
- Subjects
- *
DISTRIBUTION (Probability theory) , *STATISTICS , *PROBABILITY theory , *STATISTICAL sampling - Abstract
Abstract: We consider an i.i.d. sample, from an underlying distribution function with unknown shape, location and scale parameters, belonging to some max-domain of attraction. We study the performance of a test statistic which is merely a ratio between the maximum and the mean of the sample of the excesses above some random threshold. This scale/location invariant ratio turns out to be very useful in the construction of an asymptotically size test for the null hypothesis that the distribution comes from the Gumbel domain of attraction. The test is based on the largest observations, where is any intermediate sequence of positive integers. Both power of the test and type I error probability are studied for finite sample sizes by simulation. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
16. Data driven choice of control charts
- Author
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Albers, Willem, Kallenberg, W.C.M., and Nurdiati, Sri
- Subjects
- *
QUALITY control charts , *CHARTS, diagrams, etc. , *QUALITY control , *CONTROL theory (Engineering) - Abstract
Abstract: Standard control charts are often seriously in error when the distributional form of the observations differs from normality. Recently, control charts have been developed for larger parametric families. A third possibility is to apply a suitable (modified version of a) nonparametric control chart. This paper deals with the question when to switch from the control chart based on normality to a parametric control chart, or even to a nonparametric one. This model selection problem is solved by using the estimated model error as yardstick. It is shown that the new combined control chart asymptotically behaves as each of the specific control charts in their own domain. Simulations exhibit that the combined control chart performs very well under a great variety of distributions and hence it is recommended as an omnibus control chart, nicely adapted to the distribution at hand. The combined control chart is illustrated by an application on real data. The new modified nonparametric control chart is an attractive alternative and can be recommended as well. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
17. Estimating the retransformed mean in a heteroscedastic two-part model
- Author
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Welsh, A.H. and Zhou, X.H.
- Subjects
- *
REGRESSION analysis , *MATHEMATICAL statistics , *ANALYSIS of variance , *MEDICAL care - Abstract
Abstract: Two distribution-free estimators are proposed to estimate the mean of a dependent variable after fitting a semiparametric two-part heteroscedastic regression model to a transformation of the dependent variable. We show that the proposed estimators are consistent and have asymptotic normal distributions. We also compare their finite-sample performance in a simulation study. Finally, we illustrate the proposed methods in a real-world example of predicting in-patient health care costs. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
18. Semiparametric lower bounds for tail index estimation
- Author
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Beirlant, Jan, Bouquiaux, Christel, and Werker, Bas J.M.
- Subjects
- *
STOCHASTIC convergence , *ASYMPTOTIC expansions , *CONCENTRATION functions , *INFINITY (Mathematics) - Abstract
Abstract: We consider estimation of the tail index parameter from i.i.d. observations in Pareto and Weibull type models, using a local and asymptotic approach. The slowly varying function describing the non-tail behavior of the distribution is considered as an infinite dimensional nuisance parameter. Without further regularity conditions, we derive a local asymptotic normality (LAN) result for suitably chosen parametric submodels of the full semiparametric model. From this result, we immediately obtain the optimal rate of convergence of tail index parameter estimators for more specific models previously studied. On top of the optimal rate of convergence, our LAN result also gives the minimal limiting variance of estimators (regular for our parametric model) through the convolution theorem. We show that the classical Hill estimator is regular for the submodels introduced with limiting variance equal to the induced convolution theorem bound. We also discuss the Weibull model in this respect. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
19. Reinsurance of large claims
- Author
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Ladoucette, Sophie A. and Teugels, Jef L.
- Subjects
- *
REINSURANCE , *DISTRIBUTION (Probability theory) , *DECISION making , *RANDOM variables - Abstract
Abstract: The large claims reinsurance treaties ECOMOR and LCR are well known not to be very popular. They have been largely neglected by most reinsurers because of their technical complexity. In this paper, we derive new mathematical results connected to asymptotic problems of these reinsurance forms. Perhaps these results can reopen the discussion on the usefulness of including the largest claims in the decision making procedure. Apart from asymptotic estimates for the tail of the distribution of the ECOMOR-quantity, we find its weak laws. We also deal with the weak laws of the LCR-quantity. Finally, we illustrate the outcomes with a number of simulations. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
20. Likelihood-based confidence interval for the ratio of scale parameters of two independent Weibull distributions
- Author
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Wu, J., Wong, A.C.M., and Ng, K.W.
- Subjects
- *
WEIBULL distribution , *DISTRIBUTION (Probability theory) , *CONFIDENCE intervals , *STATISTICAL hypothesis testing - Abstract
Abstract: The Weibull distribution is widely used in lifetime data analysis. For example, in studies on the time to the occurrence of tumors in human populations or in laboratory animals, the time of occurrence of tumors is generally assumed to be distributed as a Weibull distribution. Moreover, in engineering, the voltage levels at which failure occurred in electrical cable insulation has been shown to be distributed as a Weibull distribution. When comparing two independent Weibull distributions, it is often assumed that only the scale parameter is altered. In this paper, we propose a simple and accurate procedure to obtain inference concerning the ratio of the two scale parameters of two independent distributions. The performance of the proposed method is assessed through Monte Carlo simulation studies. The numerical results show that the proposed method is extremely accurate even for very small samples. The method is applied to a set of real-life data. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
21. Exact bounds for the mean of total time on test under type II censoring samples
- Author
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Raqab, Mohammad Z.
- Subjects
- *
NONPARAMETRIC statistics , *CLUSTER analysis (Statistics) , *DISTRIBUTION (Probability theory) , *MULTIVARIATE analysis - Abstract
Abstract: This paper provides upper sharp bounds for the mean of the total time on test based on type II censoring samples in terms of various scale units. It also presents numerical evaluation of the so obtained bounds. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
22. Distribution-free bounds for expectations of increments of records
- Author
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Danielak, Katarzyna
- Subjects
- *
DISTRIBUTION (Probability theory) , *MONOTONE operators , *OPERATOR theory , *CHARACTERISTIC functions - Abstract
Abstract: Assume that are iid rv''s with continuous cumulative distribution function and finite th absolute moment. The aim of the paper is to present sharp upper bounds for expectations of increments of record values, measured in various scale units. We also derive the bounds in case when the parent distribution has monotone density and or monotone failure rate. The distribution functions attaining the bounds are characterized. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
23. Projection <f>P</f>-norm bounds on the moments of <f>K</f>th record increments
- Author
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Raqab, Mohammad Z.
- Subjects
- *
MONOTONE operators , *OPERATOR theory , *FUNCTIONAL analysis , *ALMOST periodic operators - Abstract
The projection method is applied to establish sharp
p -norm bounds, measured in terms of scale units generated by absolute central population moments for the expectations of record increments. The bounds are derived based on combining the Moriguti monotone approximation of functions with the Hölder inequality applied for the proper integral representations of expected record increments. The projectionp -norm bounds are numerically evaluated and compared with other classical bounds. [Copyright &y& Elsevier]- Published
- 2004
- Full Text
- View/download PDF
24. Second-order expansion for the maximum of some stationary Gaussian sequences
- Author
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Barbe, Ph. and McCormick, W.P.
- Subjects
- *
GAUSSIAN processes , *NEWTON-Raphson method , *APPROXIMATION theory , *STOCHASTIC processes - Abstract
We prove a second-order approximation formula for the distribution of the largest term among an infinite moving average Gaussian sequence. The second-order correction term depends on the autocovariance function only through the second largest autocovariance. Applications to Gaussian time series are discussed and a simulation study showed a substantial improvement over other approximations to the exact distribution of the maximum. [Copyright &y& Elsevier]
- Published
- 2004
- Full Text
- View/download PDF
25. Estimating an endpoint with high order moments in the Weibull domain of attraction
- Author
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Girard, Stéphane, Guillou, Armelle, and Stupfler, Gilles
- Subjects
- *
WEIBULL distribution , *ESTIMATION theory , *DIFFERENCE equations , *ASYMPTOTIC normality , *ASYMPTOTIC distribution , *MATHEMATICAL analysis - Abstract
Abstract: We present a method for estimating the endpoint of a unidimensional sample when the distribution function belongs to the Weibull-max domain of attraction. The approach relies on transforming the variable of interest and then using high order moments of the positive variable obtained this way. It is assumed that the order of the moments goes to infinity. We give conditions on the rate of divergence to get the weak and strong consistency as well as the asymptotic normality of the estimator. The good performance of the estimator is illustrated on some finite sample situations. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
26. Limit distribution of a roundoff error
- Author
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Shimura, Takaaki
- Subjects
- *
LIMIT theorems , *DISTRIBUTION (Probability theory) , *ROUNDING errors , *EXTREMAL problems (Mathematics) , *CONTINUOUS functions , *MATHEMATICAL statistics - Abstract
Abstract: Let and be the integer and the fractional parts of a random variable . The conditional distribution function for an integer is investigated. for a large is regarded as the distribution of a roundoff error in an extremal event. For most well-known continuous distributions, it is shown that converges as and three types of limit distributions appear as the limit distribution according to the tail behavior of . [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
27. Modeling the yearly Value-at-Risk for operational risk in Chinese commercial banks
- Author
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Lu, Zhaoyang
- Subjects
- *
OPERATIONAL risk , *BANKING industry , *ACQUISITION of data , *SIMULATION methods & models , *MEASURE theory , *COPULA functions - Abstract
Abstract: In this paper, we explore the loss data collection exercise for operational risk in Chinese commercial banks from 1999 to first half of 2006. Firstly, the above data are bootstrapped to analyze the capital allocation for a medium-scaled commercial bank in China. Secondly, for every selected cell, we calibrate two truncated distributions to fit the loss severity, one for ‘normal’ losses and the other for the ‘extreme’ losses. Moreover, a more realistic dependence structure – multivariate t copula function is used to measure the relation among the selected cells. In the final, the simulation results suggest that substantial savings can be achieved through measuring the dependence by means of multivariate t copula function than by means of perfect positive dependence. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
28. Weighted least squares estimation of the extreme value index
- Author
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Hüsler, Jürg, Li, Deyuan, and Müller, Samuel
- Subjects
- *
LEAST squares , *ASYMPTOTIC expansions , *MATHEMATICAL statistics , *STATISTICAL correlation - Abstract
Abstract: In this paper we present the weighted least squares estimator for the extreme value index, and prove its consistency and asymptotic normality. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
29. Asymptotics for products of independent sums with an application to Wishart determinants
- Author
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Rempała, Grzegorz and Wesołowski, Jacek
- Subjects
- *
LIMIT theorems , *STATISTICS , *MATRICES (Mathematics) , *RANDOM variables - Abstract
Abstract: We derive a lognormal limit theorem for products of independent sums of positive random variables or, in general, products of non-degenerate independent U-statistics. An application of the result gives a limit theorem for the determinant of a Wishart matrix. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
30. Reiss and Thomas’ automatic selection of the number of extremes
- Author
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Neves, Cláudia and Fraga Alves, M.I.
- Subjects
- *
PROBLEM solving , *HEURISTIC , *OPERATIONS research , *METHODOLOGY - Abstract
Most widely used semi-parametric estimators of the extreme value parameter depend on the number of upper extremes which locate where the tail of a distribution begins. In the presence of a random sample with finite size, the problem concerning the choice of the number of upper extremes is not easy to handle. This number
k is not only governed by the sample sizen , but also ruled by parameters characterizingF . When the underlying distribution function is known, the optimum valuek can be attained through the minimization of the asymptotic mean squared error of the considered estimator. Nevertheless, the merit of such procedure may be compromised by the assessment ofk values equaling the sample sizen . An alternative procedure entails that the adequate numberk should be the value which minimizes a mean distance encapsulating a penalty term just as presented by Reiss and Thomas (Statistical Analysis of Extreme Values, Birkhäuser, Basel, 1997, P. 121). The performance evaluation of Reiss and Thomas’ heuristic procedure will be carried out undertaking the asymptotically determinedk values as a reference. [Copyright &y& Elsevier]- Published
- 2004
- Full Text
- View/download PDF
31. Sharp bounds on expectations of kth record spacings from restricted families
- Author
-
Danielak, Katarzyna and Raqab, Mohammad Z.
- Subjects
- *
STATISTICS , *CONTAGIOUS distributions , *DISTRIBUTION (Probability theory) , *PROBABILITY theory - Abstract
Abstract: We derive sharp upper bounds on expectations of increments of consecutive kth record statistics based on independent samples from restricted families of distributions: the ones with decreasing density and failure rate. The results are obtained by means of projection method. [Copyright &y& Elsevier]
- Published
- 2004
- Full Text
- View/download PDF
32. On the power of the Kolmogorov test to detect the trend of a Brownian bridge with applications to a change-point problem in regression models
- Author
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Bischoff, Wolfgang, Hashorva, Enkelejd, Hüsler, Jürg, and Miller, Frank
- Subjects
- *
CHANGE-point problems , *BROWNIAN bridges (Mathematics) , *KOLMOGOROV complexity , *MATHEMATICS - Abstract
Given a Brownian bridge
B0 with trendg:[0,1]→[0,∞) ,(1) Y(z)=g(z)+B0(z),z∈[0,1],we are interested in testingH0:g≡0 against the alternativeK:g>0 . For this test problem we study weighted Kolmogorov testsreject H0⇔suplower limit z∈[0,1] w(z)Y(z)>c,wherec>0 is a suitable constant andw:[0,1]→[0,∞) is a weight function. To do such an investigation a recent result of the authors on a boundary crossing probability of the Brownian bridge is useful. In case the trend is large enough we show an optimality property for weighted Kolmogorov tests. Furthermore, an additional property for weighted Kolmogorov tests is shown which is useful to find the more favourable weight for specific test problems. Finally, we transfer our results to the change-point problem whether a regression function is or is not constant during a certain period. [Copyright &y& Elsevier]- Published
- 2004
- Full Text
- View/download PDF
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