Strong consistency of least squares estimates with i.i.d. errors with mean values not necessarily defined

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6 Citations (Scopus)

Abstract

We establish strong consistency of the least squares estimates in multiple regression models discarding the usual assumption of the errors having null mean value. Thus, we required them to be i.i.d. with absolute moment of order r, 01. Only moderately restrictive conditions are imposed on the model matrix. In our treatment, we use an extension of the Marcinkiewicz-Zygmund strong law to overcome the errors mean value not being defined. In this way, we get a unified treatment for the case of i.i.d. errors extending the results of some previous papers.

Original languageEnglish
Pages (from-to)707-714
Number of pages8
JournalStatistics
Volume47
Issue number4
DOIs
Publication statusPublished - Aug 2013

Keywords

  • least squares estimates
  • Marcinkiewicz-Zygmund law
  • regression models
  • strong consistency
  • undefined errors mean values

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