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Local maximum likelihood estimation and inference
Authors:J. Fan,M. Farmen,&   I. Gijbels
Affiliation:University of North Carolina, Chapel Hill, and University of California, Los Angeles, USA,;Abbott Laboratories, Columbus, USA,;UniversitéCatholique de Louvain, Louvain-la-Neuve, Belgium
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.
Keywords:Bandwidth selection    Confidence intervals    Generalized linear models    Logit regression    Maximum likelihood    Nonparametric regression
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