Nonparametric estimation of quadratic regression fimctionals

Li Shan Huang, F. A.N. Jianqing

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

Quadratic regression functionals are important for bandwidth selection of nonparametric regression techniques and for nonparametric goodness-of-fit tests. Based on local polynomial regression, \ve propose estimators for weighted integrals of squared derivatives of regression functions. The rates of convergence in mean square error are calculated under various degrees of smoothness and appropriate values of the smoothing parameter. Asymptotic distributions of the proposed quadratic estimators are considered with the Gaussian noise assumption. It is shown that when the estimators are pseudoquadratic (linear components dominate quadratic components), asymptotic normality with rate n~1/2 can be achieved.

Original languageEnglish (US)
Pages (from-to)927-949
Number of pages23
JournalBernoulli
Volume5
Issue number5
DOIs
StatePublished - Jan 1 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Keywords

  • Asymptotic normality
  • Equivalent kernel
  • Local polynomial regression

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