Pointwise Estimation of Density of Heteroscedastistic Response in Regression

Abstract

In fitting a regression model, we often encounter data sets which do not follow Gaussian distribution and/or do not have equal variance. In this case estimation of the conditional density of a response variable at a given design point is hardly solved by a standard least squares method. To solve this problem, we propose a simple method to estimate the distribution of the fitted vales under heteroscedasticity using the idea of quantile regression and the histogram techniques. Application of this method to a real data sets is given.