Asymptotic normality for -norm kernel estimator of conditional median under association dependence

Let { X i , Y i } i = 1 ∞ be a set of observations from a stationary jointly associated process and 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 ) based on the L 1 -norm kernel and establish asymptotic normality of the resulting estimator θ n ( x ) .