NEAREST NEIGHBOR MEDIAN ESTIMATION OF REGRESSION FUNCTION AND ITS DERIVATIVES

Abstract

Consider the fixed-design nonparametric median regression model $Y_i=g(x_i)+e_i,\,i\geq 1$. For estimating the regression function $g(x)$ and its derivative, the nearest neighbor median estimators $\tilde{g}_{n,h}(x)$ are employed, where $h$ is the number of the nearest neighbors. Under mild regularity conditions, rates of convergence for the estimators are obtained.