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≤yX=x)≥1/2}. We consider the problem of estimating θ(x) from the data (X₁, Y₁), ..., (X_n, Y_n) 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.