摘要
设x_n的密度函数为f(x),X∈R^d,f_n(x)=(nh^d)^(-1)sum from i-1 to n k((x-x_i)/h)为f的核估计,其中0<h=h(n)→0,K绝对可积且∫K(x)dx=1,记J_n=∫|f_n(x)-f(x)|dx,本文对样本{x_n}为α混合或φ混合时.给出J_n依概率趋于0,完全收敛于0的充分条件。
Let f be a density on R^d and f_n be the kernel estimate of f, f_n (x) = (nh^d)^(-1) sum from i=1 to n K ((x-x_i)/h), where h=h_n→0 and K is an absolutely integrable function with ∫k(x)dx=1. Let J_n= f|f_n(x)-f(x)|dxwe give some sufficient conditions for J_n→0 in probability or J_n→0 complete- ly, where {x_n) is α-mixing or φ-mixing sample, which generalize the result in.
出处
《安徽大学学报（自然科学版）》
CAS
1993年第2期11-17,共7页
Journal of Anhui University(Natural Science Edition)
关键词
核密度估计
弱相合性
完全相合性
kernel density estimate
weak consistency
complete consistency
