DOUBLE KERNEL ESTIMATORS OF CONDITION DENSITY OF STATIONARY PROCESSES

Let （X_n, Y_n）; n≥1 be R^p×R^q-valued random vectors sequence of stationary processes φ-Mixing having common joint density g（x, y）, Let h（x） be the marginal density of X₁ and Let f（y|x）=g（x, y）/ h（x） be the conditional density of Y₂ on X₁, then the double kernel estimates of f（y|x） is defined by f_n(y \mid x)=\sum_i=1^n K_1\left(\fracx-X_ia_n\right) K_2\left(\fracy-Y_ib_n\right) /\leftb_n^q \sum_i=1^n K_1\left(\fracx-X_ia_n\right)\right,where K₁ and K₂ are probability density function on R^p and R^q. respectively and both α_n and b_n are sequences of positive numbers converging to zero. In the paper, we study the pointwise consistency and asymptotic normality of f_n(y|x)under the case of dependent asmple.