相依样本下条件密度的双重核估计

DOUBLE KERNEL ESTIMATORS OF CONDITIONAL DENSITY UNDER DEPENDENT SAMPLES

本文在样本序列为平稳φ-混合的情形下,研究了条件密度f(y|x)的通常的和递推形式的双重核估计的强相合性,并给出了它们的强收敛速度以及渐近分布.

Let ( X1 ,Y1), …, (Xn,Yn ) be random samples taken in Rp × Rq and f ( y | x) be the conditional density function of Y1 on X1 . In the paper, we consider the double kernel estimates of f(y|x):where K1 and K2 are probability density functions on Rp and Rq respectively, and both {an} and {bn} are sequences of positive numbers converging to zero. We study the strong consistency of fn(y|x) and fn(i)(y|x) under the condition when { (Xn, Yn) } is a sequence of stationary (?)-mixed variable, and we give its strong convergence rates and asymptotic distribution.