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Minimum distance estimation in linear models with long range dependent errors.

Research output: Contribution to journalJournal article

Published

Journal publication date7/12/1994
JournalStatistics and Probability Letters
Journal number5
Volume21
Number of pages9
Pages347-355
Original languageEnglish

Abstract

This paper discusses the asymptotic representations of a class of L2-distance estimators based on weighted empirical processes in a multiple linear regression model when the errors are a function of stationary Gaussian random variables that are long-range dependent. Unlike the independent errors case, the limiting distributions of the suitably normalized estimators are not always normal. The limiting distributions depend heavily on the Hermite rank of a certain class of random variables. Some ‘goodness of fit’ tests for specified error distribution are also considered.