NONPARAMETRIC ESTIMATION OF THE CONDITIONAL MEDIAN FUNCTION FOR LONG-RANGE DEPENDENT PROCESSES

Abstract

This paper considers the problem of estimating the conditional median of Y_i=v(X_i)+ε_i, given X_i=x. We assume{X_i}and{ε_i}are independent linear processes with long-range dependence, estimate the conditional median by local LAD regression, and show the asymptotic normality of the estimator. The asymptotic property depends on the degree of dependence. When the dependence is not very strong, the asymptotic behavior is the same as in the case of weakly dependent processes. When the dependence is very strong, the estimator behaves as the estimator of the conditional mean function, and the effect of long-range dependence apoears.