Nonparametric Estimation of a Regression Function: Limiting Distribution

Kuang‐Fu ‐F Cheng, Pi‐Erh ‐E Lin

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12 Citations (Scopus)

Abstract

Consider the regression model Yi= g(xi) + ei, i = 1,…, n, where g is an unknown function defined on [0, 1], 0 = x0 < x1 < … < xn≤ 1 are chosen so that max1≤i≤n(xi‐xi‐ 1) = 0(n‐1), and where {ei} are i.i.d. with Ee1= 0 and Var e1 ‐ s̀2. In a previous paper, Cheng & Lin (1979) study three estimators of g, namely, g1n of Cheng & Lin (1979), g2n of Clark (1977), and g3n of Priestley & Chao (1972). Consistency results are established and rates of strong uniform convergence are obtained. In the current investigation the limiting distribution of &in, i = 1, 2, 3, and that of the isotonic estimator g**n are considered.

Original languageEnglish
Pages (from-to)186-195
Number of pages10
JournalAustralian Journal of Statistics
Volume23
Issue number2
DOIs
Publication statusPublished - 1981
Externally publishedYes

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Keywords

  • Asymptotic normality
  • Berry‐Esséen bound
  • Isotonic
  • Kernel function
  • Liapunov's theorem
  • Lipschitz
  • phrases

ASJC Scopus subject areas

  • Statistics and Probability

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