Empirical likelihood inferences for the semiparametric additive isotonic regression

Abstract

We consider the (profile) empirical likelihood inferences for the regression parameter (and its any sub-component) in the semiparametric additive isotonic regression model where each additive nonparametric component is assumed to be a monotone function. In theory, we show that the empirical log-likelihood ratio for the regression parameters weakly converges to a standard chi-squared distribution. In addition, our simulation studies demonstrate the empirical advantages of the proposed empirical likelihood method over the normal approximation method in Cheng (2009) [4] in terms of more accurate coverage probability when the sample size is small. It is worthy pointing out that we can construct the empirical likelihood based confidence region without the hassle of tuning any smoothing parameter due to the shape constraints assumed in this paper.