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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...

The asymptotic distribution of the bootstrap sample mean of an infinitesimal array

J. A. Cuesta-Albertos, C. Matrán (1998)

Annales de l'I.H.P. Probabilités et statistiques

The Asymptotic Properties of Maximum Likelihood Estimators for Marked Poisson Processes with a Cyclic Intensity Measure.

F. Konecny (1987)

Metrika

The Berry-Esseen Bound for Minimum Contrast Estimators in the Independent not Identically Distributed Case.

B.L.S. Prakasa Rao (1975)

Metrika

The bootstrap of the mean with arbitrary bootstrap sample size

Miguel A. Arcones, Evarist Giné (1989)

Annales de l'I.H.P. Probabilités et statistiques

The Central Limit Theorem for Maximum Likelihood Estimators of Vector Parameters: Locally Uniform Convergence.

R. Michel (1977/1978)

Manuscripta mathematica

The least trimmed squares. Part I: Consistency

Jan Ámos Víšek (2006)

Kybernetika

The consistency of the least trimmed squares estimator (see Rousseeuw [Rous] or Hampel et al. [HamRonRouSta]) is proved under general conditions. The assumptions employed in paper are discussed in details to clarify the consequences for the applications.

The least trimmed squares. Part II: $\sqrt{n}$ -consistency

Jan Ámos Víšek (2006)

Kybernetika

$\sqrt{n}$ -consistency of the least trimmed squares estimator is proved under general conditions. The proof is based on deriving the asymptotic linearity of normal equations.

The least trimmed squares. Part III: Asymptotic normality

Jan Ámos Víšek (2006)

Kybernetika

Asymptotic normality of the least trimmed squares estimator is proved under general conditions. At the end of paper a discussion of applicability of the estimator (including the discussion of algorithm for its evaluation) is offered.

The likelihood ratio test for general mixture models with or without structural parameter

Jean-Marc Azaïs, Élisabeth Gassiat, Cécile Mercadier (2009)

ESAIM: Probability and Statistics

This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRT statistics under some conditions that are proved to be almost necessary. A detailed solution is given for two testing problems: the test of a single distribution against any mixture, with application to Gaussian, Poisson and binomial distributions; the test of the number of populations...

The role of Hájek's convolution theorem in statistical theory

Rudolf Beran (1995)

Kybernetika

The two-dimensional linear relation in the errors-in-variables model with replication of one variable

Anna Czapkiewicz, Antoni Dawidowicz (2000)

Applicationes Mathematicae

We present a two-dimensional linear regression model where both variables are subject to error. We discuss a model where one variable of each pair of observables is repeated. We suggest two methods to construct consistent estimators: the maximum likelihood method and the method which applies variance components theory. We study asymptotic properties of these estimators. We prove that the asymptotic variances of the estimators of regression slopes for both methods are comparable.

Third-Order Optimum Properties of Estimator-Sequences.

Th. Pfaff (1983)

Metrika

Variance function estimation via model selection

Teresa Ledwina, Jan Mielniczuk (2010)

Applicationes Mathematicae

The problem of estimating an unknown variance function in a random design Gaussian heteroscedastic regression model is considered. Both the regression function and the logarithm of the variance function are modelled by piecewise polynomials. A finite collection of such parametric models based on a family of partitions of support of an explanatory variable is studied. Penalized model selection criteria as well as post-model-selection estimates are introduced based on Maximum Likelihood (ML) and Restricted...