M-estimators in linear models with long range dependent errors
type: Item
instance of: scholarly article
title: M-estimators in linear models with long range dependent errors
zbMATH Open document ID: 0759.62023
DOI: 10.1016/0167-7152(92)90079-K
published in: Statistics \& Probability Letters
publication date: 1993-01-16T00:00:00Z
review text: The author considers the linear model \(Y_ i=X_ i'\beta+\varepsilon_ i\), where \(\{Y_ i\}\) is an observable process, \(X_ i'=(1,\xi_ i')\), is an observable \(p\times 1\) stationary mean zero random vector process, \(\beta\) is an unknown constant vector and \(\{\varepsilon_ i\}\) is a measurable transformation of a strictly stationary mean zero, unit variance Gaussian process \(\{\eta_ i\}\). He assumes long range dependence of \(\{\xi_ i\}\) and \(\{\eta_ i\}\) and considers an \(M\)- estimator \(\hat\beta_ N\) of \(\beta\). Under some conditions, he evaluates the asymptotic behavior of \(\hat\beta_ N-\beta\) and shows some formulas concerning asymptotics. The case of non-random designs is also mentioned.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 93348
zbMATH Keywords: dependent errors
zbMATH Keywords: skew symmetric scores
zbMATH Keywords: symmetric errors
zbMATH Keywords: least squares estimator
zbMATH Keywords: asymptotic normality
zbMATH Keywords: non-normality
zbMATH Keywords: Hermite rank
zbMATH Keywords: polynomials
zbMATH Keywords: linearity
zbMATH Keywords: linear model
zbMATH Keywords: stationary mean zero random vector process
zbMATH Keywords: Gaussian process
zbMATH Keywords: long range dependence
zbMATH Keywords: \(M\)-estimator
zbMATH Keywords: non- random designs
author: Hira L. Koul
reviewed by: Mituaki Huzii
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 93348