Local maximum likelihood estimation and inference |
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Authors: | J. Fan,M. Farmen,& I. Gijbels |
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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 |
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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. |
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Keywords: | Bandwidth selection Confidence intervals Generalized linear models Logit regression Maximum likelihood Nonparametric regression |
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