Some strong consistency results in stochastic regression

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Abstract

Strong consistency of the least-squares estimates in stochastic regression models is established assuming errors with variance not necessarily defined. The errors will be considered identically distributed having absolute moment of order r, 0 <r ≤ 2 and, additionally, pairwise independent whenever r = 2. It is shown that only a moderate asymptotic assumption on the stochastic regressors is sufficient to obtain strong consistency of the least-squares estimates allowing that both exponential and linear asymptotic behavior for the squared sums of the design levels can coexist. Strong consistency of the ridge estimates is also obtained for some biasing parameters using the previous assumptions on the errors.

Original languageEnglish
Pages (from-to)220-226
Number of pages7
JournalJournal of Multivariate Analysis
Volume129
DOIs
Publication statusPublished - 2014

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Keywords

  • Least-squares estimates
  • Ridge estimates
  • Stochastic regression models
  • Strong consistency

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