The laws of the iterated logarithm of some estimates in partly linear models

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Abstract

Consider the regression model Yi = xi′β + g(ti) + ei, 1 ≤ i ≤ n, where xi = (xi1, xi2, ..., xip)′ and ti (ti ε{lunate} [0, 1]) are known and nonrandom design points, β = (β1, ..., βp)′ (p ≥ 1) is an unknown parameter, g(·) is an unknown function, and ei are i.i.d. random errors. Based on g estimated by nonparametric kernel estimation, the laws of the iterated logarithm of the least-square estimator of β and an estimator of σ2 = Ee12 < ∞ are investigated.

Original languageEnglish
Pages (from-to)153-162
Number of pages10
JournalStatistics and Probability Letters
Volume25
Issue number2
DOIs
Publication statusPublished - 1 Nov 1995

Keywords

  • Least-square estimator
  • Partly linear model
  • The law of iterated logarithm

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