COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1792 Empirical Likelihood for Nonparametric Additive Models Taisuke Otsu April 2011 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. |
