密度泛函估计的重对数律,中心极限定理和不变原理
A LAW OF THE ITERATED LOGARITHM, A DENTRAL LIMIT THEOREM AND AN INVARIANCE PRINCIPLE FOR ESTIMATORS OF FUNCTIONALS OF DENSITY
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摘要: 设X1,…,Xn是从分布密度为f(单变量实值函数)的总体中抽出的iid.样本.μ=EX1。本文研究了密度泛函θ=f(μ)的核型估计f_n(\barX)\left(\barX=\sum_i=1^n X_i / n\right.,\hatf_n(x)为通常的Rosenblatt-Parzen核估计)的大样本性质。Abstract: In this pauer we study the asympotatic behavior of kernel type estimator of the unknown deosity evaluated at a random point and establish the LIL, CLT and IP for such estima tor under oertain oonditions.