Tail-behaviour of location estimators in non-regular cases
Tauberian and Abelian theorems for rapidly decaying distributions and their applications to stable laws.
Test of Hypotheses in some Families of Discrete Distributions
Testing a homogeneity of stochastic processes
The paper concentrates on modeling the data that can be described by a homogeneous or non-homogeneous Poisson process. The goal is to decide whether the intensity of the process is constant or not. In technical practice, e.g., it means to decide whether the reliability of the system remains the same or if it is improving or deteriorating. We assume two situations. First, when only the counts of events are known and, second, when the times between the events are available. Several statistical tests...
Testing a sub-hypothesis in linear regression models with long memory covariates and errors
This paper considers the problem of testing a sub-hypothesis in homoscedastic linear regression models when the covariate and error processes form independent long memory moving averages. The asymptotic null distribution of the likelihood ratio type test based on Whittle quadratic forms is shown to be a chi-square distribution. Additionally, the estimators of the slope parameters obtained by minimizing the Whittle dispersion is seen to be -consistent for all values of the long memory parameters...
Testing a tolerance hypothesis by means of an information distance
In the paper a test of the hypothesis , on parameters of the normal distribution is presented, and explicit formulas for critical regions are derived for finite sample sizes. Asymptotic null distribution of the test statistic is investigated under the assumption, that the true distribution possesses the fourth moment.
Testing in locally conic models, and application to mixture models
Testing in locally conic models, and application to mixture models
In this paper, we address the problem of testing hypotheses using maximum likelihood statistics in non identifiable models. We derive the asymptotic distribution under very general assumptions. The key idea is a local reparameterization, depending on the underlying distribution, which is called locally conic. This method enlights how the general model induces the structure of the limiting distribution in terms of dimensionality of some derivative space. We present various applications of...
Tests for the presence of trends in linear processes [Book]
Tests of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions
Test statistics for testing some hypotheses on characteristic roots of covariance matrices are presented, their asymptotic distribution is derived and a confidence interval for the proportional sum of the characteristic roots is constructed. The resulting procedures are robust against violation of the normality assumptions in the sense that they asymptotically possess chosen significance level provided that the population characteristic roots are distinct and the covariance matrices of certain quadratic...
The asymptotic distribution of the bootstrap sample mean of an infinitesimal array
The asymptotic distributions of statistics based on logarithms of spacings
The Asymptotic Properties of Maximum Likelihood Estimators for Marked Poisson Processes with a Cyclic Intensity Measure.
The Berry-Esseen Bound for Minimum Contrast Estimators in the Independent not Identically Distributed Case.
The Berry-Esseen theorem for rank statistics
The Berry-Esséen Theorem for the Subject-Years Method in Mortality Analysis with Censored Data.
The beta Gumbel distribution.
The bootstrap of the mean with arbitrary bootstrap sample size
The Bound in the Berry-Esseen Result for Minimum Contrast Estimates.
The Central Limit Theorem for Maximum Likelihood Estimators of Vector Parameters: Locally Uniform Convergence.