JOURNAL OF THE JAPAN STATISTICAL SOCIETY
Online ISSN : 1348-6365
Print ISSN : 1882-2754
ISSN-L : 1348-6365
Articles
Empirical Likelihood for Nonparametric Additive Models
Taisuke Otsu
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JOURNAL FREE ACCESS

2012 Volume 41 Issue 2 Pages 159-186

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Abstract

Nonparametric additive modeling is a fundamental tool for statistical data analysis which allows flexible functional forms for conditional mean or quantile functions but avoids the curse of dimensionality for fully nonparametric methods induced by high-dimensional covariates. This paper proposes empirical likelihood-based inference methods for unknown functions in three types of nonparametric additive models: (i) additive mean regression with the identity link function, (ii) generalized additive mean regression with a known non-identity link function, and (iii) additive quantile regression. The proposed empirical likelihood ratio statistics for the unknown functions are asymptotically pivotal and converge to chi-square distributions, and their associated confidence intervals possess several attractive features compared to the conventional Wald-type confidence intervals.

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© 2012 Japan Statistical Society
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