The limit distribution of weighted \(L^2\)-goodness-of-fit statistics under fixed alternatives, with applications

DOI10.1007/s10463-016-0567-8zbMath1422.62077OpenAlexW2423539830MaRDI QIDQ1680796

Ludwig Baringhaus, Bruno Ebner, Norbert Henze

Publication date: 16 November 2017

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10463-016-0567-8

zbMATH Keywords

goodness-of-fit testasymptotic confidence intervalsfixed alternativeasymptotic equivalence testempirical transformweighted \(L^2\)-statistic

Mathematics Subject Classification ID

Gaussian processes (60G15) Asymptotic distribution theory in statistics (62E20) Nonparametric tolerance and confidence regions (62G15)

Related Items (27)

A new omnibus test of fit based on a characterization of the uniform distribution ⋮ Tests for circular symmetry of complex-valued random vectors ⋮ On a test of normality based on the empirical moment generating function ⋮ Comments on: ``Tests for multivariate normality -- a critical review with emphasis on weighted \(L^2\)-statistics ⋮ Rejoinder on: ``Tests for multivariate normality -- a critical review with emphasis on weighted \(L^2\)-statistics ⋮ Testing normality via a distributional fixed point property in the Stein characterization ⋮ On combining the zero bias transform and the empirical characteristic function to test normality ⋮ On a new goodness-of-fit test for the Rayleigh distribution based on a conditional expectation characterization ⋮ More good news on the HKM test for multivariate reflected symmetry about an unknown centre ⋮ A general Monte Carlo method for multivariate goodness-of-fit testing applied to elliptical families ⋮ A weighted integral approach to testing against HNBUE alternatives ⋮ Testing normality in any dimension by Fourier methods in a multivariate Stein equation ⋮ The test of exponentiality based on the mean residual life function revisited ⋮ Logistic or not Logistic? ⋮ Bahadur efficiencies of the Epps-Pulley test for normality ⋮ Integral transform methods in goodness-of-fit testing. I: The gamma distributions ⋮ CHARACTERIZATIONS OF MULTINORMALITY AND CORRESPONDING TESTS OF FIT, INCLUDING FOR GARCH MODELS ⋮ Statistical inference for \(L^2\)-distances to uniformity ⋮ Sample size determination of a nonparametric test based on weighted \(L_2\)-Wasserstein distance ⋮ A new class of tests for multinormality with i.i.d. And garch data based on the empirical moment generating function ⋮ Integral transform methods in goodness-of-fit testing. II: The Wishart distributions ⋮ A new test of multivariate normality by a double estimation in a characterizing PDE ⋮ Tests for multivariate normality -- a critical review with emphasis on weighted $L^2$-statistics ⋮ A new characterization of the Gamma distribution and associated goodness-of-fit tests ⋮ Inferential procedures based on the integrated empirical characteristic function ⋮ Equivalence tests for multinomial data based on \(\phi\)-divergences ⋮ New classes of tests for the Weibull distribution using Stein's method in the presence of random right censoring

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Goodness-of-Fit Tests for the Gamma Distribution Based on the Empirical Laplace Transform
• Characteristic function-based hypothesis tests under weak dependence
• Testing for the bivariate Poisson distribution
• Probability in Banach spaces. Isoperimetry and processes
• Testing for symmetry in multivariate distributions
• Tests of fit for normal inverse Gaussian distributions
• Goodness-of-fit tests for copulas
• A goodness-of-fit test for bivariate extreme-value copulas
• An approximation to the limit distribution of the Epps-Pulley test statistic for normality
• Some comments on goodness-of-fit tests for the parametric form of the copula based on \(L^{2}\)-distances
• A nonparametric test for similarity of marginals -- with applications to the assessment of population bioequivalence
• A goodness of fit test for the Poisson distribution based on the empirical generating function
• A class of consistent tests for exponentiality based on the empirical Laplace transform
• A new approach to the BHEP tests for multivariate normality
• Extreme smoothing and testing for multivariate normality
• Testing for affine equivalence of elliptically symmetric distributions.
• Invariant tests for symmetry about an unspecified point based on the empirical characteristic function.
• Goodness-of-fit tests for the Cauchy distribution based on the empirical characteristic function
• Recent and classical goodness-of-fit tests for the Poisson distribution
• Recent and classical tests for exponentiality: a partial review with comparisons
• Checking the adequacy of the multivariate semiparametric location shift model
• On the effect of substituting parameter estimators in limiting \(\chi ^ 2U\) and V statistics
• Invariant tests for multivariate normality: A critical review
• Goodness-of-fit tests for the inverse Gaussian distribution based on the empirical Laplace transform
• Tests of fit for the Rayleigh distribution based on the empirical Laplace transform
• Testing skew normality via the moment generating function
• Testing for the generalized normal-Laplace distribution with applications
• A characterization and a class of omnibus tests for the exponential distribution based on the empirical characteristic function
• Test of fit for Marshall-Olkin distributions with applications
• Two-sample tests based on empirical Hankel transforms
• Goodness of fit for the poisson distribution based on the probability generating function
• A new flexible class of omnibus tests for exponentiality
• A Class of Omnibus Tests for the Laplace Distribution based on the Empirical Characteristic Function
• A Comparative Study of Several One-Sided Goodness-of-Fit Tests
• Testing for a class of bivariate exponential distributions
• Tests for the multivariatek-sample problem based on the empirical characteristic function
• A Powerful Method of Assessing the Fit of the Lognormal Distribution
• Testing Statistical Hypotheses of Equivalence and Noninferiority
• Tests for generalized exponential laws based on the empirical Mellin transform
• A class of invariant consistent tests for multivariate normality
• On the asymptotic normality of theL₂-Distance Class of Statistics with Estimated Parameters
• Some Methodological Aspects of Validation of Models in Nonparametric Regression
• Tests of Fit for Exponentiality based on the Empirical Laplace Transform
• GOODNESS-OF-FIT TESTS BASED ON A NEW CHARACTERIZATION OF THE EXPONENTIAL DISTRIBUTION
• Permutation tests for homogeneity based on the empirical characteristic function
• A test for normality based on the empirical characteristic function

This page was built for publication: The limit distribution of weighted \(L^2\)-goodness-of-fit statistics under fixed alternatives, with applications