M-Estimators in Linear Models with Long Range Dependent Errors

Abstract

This note discusses the asymptotic behavior of a class of M- estimators in linear models which errors are Gaussian, or a function of Gaussian random variables, that are long range dependent. The asymptotics are discussed when the design variables are either i.i.d. or long range dependent, independent of the errors, or known constants. It is observed that the class of M-estimators of the regression parameter vector corresponding to skew symmetric scores and symmetric errors asymptotically behave like the least squares estimators. Moreover, in these cases, if the design variables are either i.i.d. or known constants then the limiting distributions are Normal. But if the design variables are also long range dependent then the limiting distributions are nonnormal. (kr)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1990
Accession Number
ADA219921

Entities

People

  • Hira L. Koul

Organizations

  • University of North Carolina at Chapel Hill

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Communities of Interest

  • Materials and Manufacturing Processes

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Fields of Study

  • Mathematics

Readers

  • Regression Analysis.
  • Statistical inference.