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Asymptotic uniform linearity of some robust statistics under exponentially subordinated strongly dependent models

Research output: Contribution to journalJournal article

Published

Journal publication date15/08/1999
JournalStatistics and Probability Letters
Journal number2
Volume44
Number of pages10
Pages137-146
Original languageEnglish

Abstract

In this paper, we discuss an asymptotic distributional theory of three broad classes of robust estimators of the regression parameter namely, L-, M- and R-estimators in a linear regression model when the errors are generated by an exponentially
subordinated strongly dependent process. The results are obtained as a consequence of an asymptotic uniform Taylor-type expansion of certain randomly weighted empirical processes. The limiting distributions of the estimators are nonnormal and depend on the rst nonzero index of the Laguerre polynomial expansion of a class of indicator functions of the error random variables.