Asymptotic Normality for L1 Norm Kernel Estimator of Conditional Median under α-Mixing Dependence

Let (X1, Y1), (X2, Y2), …, be d+1 dimensional random vectors which are distributed as (X, Y). Let θ(x) be the conditional median, that is, θ(x)=inf{y: P(Y⩽y ∣ X=x)⩾1/2}. We consider the problem of estimating θ(x) from the data (X1, Y1), …, (Xn, Yn) which are α-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.