Strong representations for LAD estimators in linear models

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Abstract

Consider the standard linear model yi=ziβ+ei, i=1, 2,..., n, where zi denotes the ith row of an n x p design matrix, β∈ℝp is an unknown parameter to be estimated and ei are independent random variables with a common distribution function F. The least absolute deviation (LAD) estimate {Mathematical expression} of β is defined as any solution of the minimization problem {Mathematical expression} In this paper Bahadur type representations are obtained for {Mathematical expression} under very mild conditions on F near zero and on zi, i=1,..., n. These results are extended to the case, when {ei} is a mixing sequence. In particular the results are applicable when the residuals ei form a simple autoregressive process.

Original languageEnglish (US)
Pages (from-to)547-558
Number of pages12
JournalProbability Theory and Related Fields
Volume83
Issue number4
DOIs
StatePublished - Dec 1 1989

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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