φ混合序列自正则加权和的中心极限定理

Central Limit Theorem for Self-normalized Weighted Sums of φ-Mixing Sequences

设{Xn,n≥1}为一严平稳φ混合随机变量序列,EX=0,V2n=∑ni=1Xi2,{an,i,1≤i≤n,n≥1}为一实数阵列,Sn=∑ni=1an,iXi.利用随机变量阵列的弱收敛定理,在较一般的条件下,证明了自正则加权和{Sn/Vn,n≥1}的中心极限定理,改进并推广了已有混合序列自正则化中心极限定理的相关结果.

Let {Xn,n≥1}be a sequence of strictly stationary φ-mixing random variables with EX=0,V^2n=∑^n i=1 X^2i ,{an,i 1≤i≤n,n≥1}be an array of real numbers with Sn=∑^n i=1 an,i Xi.Using the weak convergence theorem of the arrays, under general conditions, we obtained the central limit theorem for self-normalized weighted sum of {Sn/Vn,n≥1}.The results about this scope are improved and extended.