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Tail approximations for samples from a finite population with applications to permutation tests

Zhishui Hu, John Robinson, Qiying Wang (2012)

ESAIM: Probability and Statistics

This paper derives an explicit approximation for the tail probability of a sum of sample values taken without replacement from an unrestricted finite population. The approximation is shown to hold under no conditions in a wide range with relative error given in terms of the standardized absolute third moment of the population, β3N. This approximation is used to obtain a result comparable to the well-known Cramér large deviation result in the independent case, but with no restrictions on the sampled...

Tail approximations for samples from a finite population with applications to permutation tests

Zhishui Hu, John Robinson, Qiying Wang (2012)

ESAIM: Probability and Statistics

This paper derives an explicit approximation for the tail probability of a sum of sample values taken without replacement from an unrestricted finite population. The approximation is shown to hold under no conditions in a wide range with relative error given in terms of the standardized absolute third moment of the population, β3N. This approximation is used to obtain a result comparable to the well-known Cramér large deviation result in the independent ...

Testing a homogeneity of stochastic processes

Jaromír Antoch, Daniela Jarušková (2007)

Kybernetika

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

Hira L. Koul, Donatas Surgailis (2008)

Applications of Mathematics

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 n 1 / 2 -consistent for all values of the long memory parameters...

Testing a tolerance hypothesis by means of an information distance

František Rublík (1990)

Aplikace matematiky

In the paper a test of the hypothesis μ + c σ ≤ M , μ - c σ ≥ m 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

Didier Dacunha-Castelle, Elisabeth Gassiat (2010)

ESAIM: Probability and Statistics

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 of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions

František Rublík (2001)

Kybernetika

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...

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