Conditional Probability Density and Regression Function Estimations With Transformation of Data

This study extends 'empirical transformation' in kernel smoothing to conditional probability density and regression function estimations. We propose nonparametric conditional probability density and regression function estimators, which are based on an extension of wik and Mielniczuk (1989)'s method. We derived asymptotic properties of the proposed estimators and conducted a simulation that showed mean squared errors of conditional probability density and regression function estimators.