Asymptotic Normality for L1 Norm Kernel Estimator of Conditional Median under [alpha]-Mixing Dependence

Let (X1, Y1), (X2, Y2), ..., be d+1 dimensional random vectors which are distributed as (X, Y). Let [theta](x) be the conditional median, that is, [theta](x)=inf{y: P(Y[less-than-or-equals, slant]y | X=x)[greater-or-equal, slanted]1/2}. We consider the problem of estimating [theta](x) from the data (X1, Y1), ..., (Xn, Yn) which are [alpha]-mixing dependence. L1-norm kernel estimators of conditional median of weakly dependent random variables are proposed and the asymptotic normality of the resulting estimators is derived.