Local maximum likelihood estimation and inference

Jianqing Fan, Mark Farmen, Irène Gijbels

Research output: Contribution to journalArticle

106 Scopus citations

Abstract

Local maximum likelihood estimation is a nonparametric counterpart of the widely used parametric maximum likelihood technique. It extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces. Associated with this nonparametric estimation scheme is the issue of bandwidth selection and bias and variance assessment. This paper provides a unified approach to selecting a bandwidth and constructing confidence intervals in local maximum likelihood estimation. The approach is then applied to least squares nonparametric regression and to nonparametric logistic regression. Our experiences in these two settings show that the general idea outlined here is powerful and encouraging.

Original languageEnglish (US)
Pages (from-to)591-608
Number of pages18
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume60
Issue number3
DOIs
StatePublished - Jan 1 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Bandwidth selection
  • Confidence intervals
  • Generalized linear models
  • Logit regression
  • Maximum likelihood
  • Nonparametric regression

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