M-type smoothing splines in nonparametric and semiparametric regression models

Jiti Gao, Peide Shi

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20 Citations (Scopus)

Abstract

Consider the regression model Y i = g(t i) + e i for i = 1,...,n. Here -∞ < Y i, e i < ∞, t i ∈ T ⊂ R d, g ∈ H, and H is a specified class of continuous functions from T to R. Based on a finite series expansion g̃ n of g, an M-estimate ĝ n of g is constructed, and the asymptotic normality of the estimate is investigated. Meanwhile, a test statistic for testing H 0 : g(·) = g 0(·) (a known function) is discussed. We also consider M-estimates for semiparametric regression models and show that they are consistent and asymptotically normal.

Original languageEnglish
Pages (from-to)1155-1169
Number of pages15
JournalStatistica Sinica
Volume7
Issue number4
Publication statusPublished - 1 Oct 1997

Keywords

  • Asymptotic normality
  • M-estimation
  • Nonparametotic regression model
  • Semiparametric regression model
  • Spline smoothing technique

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