摘要
本文在样本序列为平稳、φ-混合情形下研究了赵林城和刘志军提出的条件密度f(y|x)的双重核估计fn(y|x)的逐点强相合性和渐近正态性。我们对混合系数φ的限制是很弱的。
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 X_1 and Let f(y|x)--g(x, y)/h(x) be the conditional density of Y_2 on X_1, then the double kernel estimates of f(y|x) is defined by f_n(y|x)=sum from i=1 to n(((K_1((x-X_i)/α_n)K_2((y-Y_i)/b_n))/[b_n^q sum from i=1 to n(K_1((x-X_i)/α_n))])where K_1 and K_2 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.
出处
《应用概率统计》
CSCD
北大核心
1993年第1期41-50,共10页
Chinese Journal of Applied Probability and Statistics
