摘要
设X_1,…,X_n是一组独立的随机变量序列,设EX_i=0,VarZ_i=μ_2,i=1,2,…,n,其中μ_2是待估参数。当X_i,i=1,2,…n给定后,分别用D_n=sum from i=1 to n (V_i(X_i-X)~2)-(1/n) sum from i=1 to n (X_i-X)~2及U_n=sum from i=1 to n (V_i(X_i-sum from i=1 to n V_iX_i)~2)-(1/n) sum from i=1 to n (X_i-X)~2两种形式的随机加权分布来逼近T_n=(1/n)sum from i=1 to n (X_i-X)~2-μ_2的分布,这里(V_1,…,V_n)是服从Dirichlet分布D(4,…,4)的随机向量。若记F_n是T_n/(VarT_n^(1/2))的分布,F_n~*,G_n~*分别是给定X_1,…,X_n条件下,D_n/(Var~*D_n^(1/2))和U_n/(Var~*U_n^(1/2))的条件分布。Var~*是关于X_1,…,X_n的条件方差。则在一定的条件下,对几乎所有的样本序列X_1,…,X_n (i)lim n^(1/2)(n→∞) sup |F_n~*(y)-F_n(y)|=0 (-∞<y<∞) (ii)lim n^(1/2)(n→∞) sup |G_n~*(y)-F_n(y)|=0 (-∞<y<∞)
The random weighting method which differs from Bootstrap ,is a new approach to estimate of the distribution of pivotal statistics .In this paper ,we develop an Edgeworth expansion for the random weighting distribution of sample variance when the sample has not the independent identicaly distribution .Let Fn(y) bethe distribution function of , Fn(y) be the distribution function ofand Gn(y) be the distribution function ofin suitable conditions ,we have
