Asymptotic results in gamma kernel regression

Abstract

Based on the Gamma kernel density estimation procedure, this article constructs a nonparametric kernel estimate for the regression functions when the covariate are nonnegative. Asymptotic normality and uniform almost sure convergence results for the new estimator are systematically studied, and the finite performance of the proposed estimate is discussed via a simulation study and a comparison study with an existing method. Finally, the proposed estimation procedure is applied to the Geyser data set.