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Empirical Likelihood for Nonparametric Additive Models

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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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File URL: http://cowles.econ.yale.edu/P/cd/d17b/d1792.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1792.

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Length: 28 pages
Date of creation: Apr 2011
Date of revision:
Handle: RePEc:cwl:cwldpp:1792

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Nonparametric additive model; Empirical likelihood; Generalized linear model; Quantile regression;

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  1. De Gooijer J.G. & Zerom D., 2003. "On Additive Conditional Quantiles With High Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 135-146, January.
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