摘要
设{d_(ni),i=1,…,n},{X_(ni),i=1,…,n}分别为双下标常数列和随机变量列。众所周知,有关sum from i=1 to n (d_(ni)X_(ni))的收敛性问题,在统计推断中有着广泛的应用,例如在异方差的回归分析中的重要应用[3]。当{X_(ni),F_(ni),-∞<i<∞}为鞅差序列时,文献[4]研究了sum from i X_(ni)的渐进正态性,本文获得sum from i=1 to n (d_(ni)X_(ni))的P阶均方收敛及强收敛于零的充分条件,其中{X_(ni),i=1,…,n}为局部广义高斯序列或L^p混合序列。
Let {dni,i =1,…, n} and {Xni,i = 1,…, n} be a double array of constants and a. random variables,respectively. We discuss the pth- mean and strong consistency of theweight sums sum from i=1 to n dniXni, the randum part {Xni,i = 1,…,n} are assumed to be eitheran Lp mixingale or generalized Gaussion. Our results are useful in regression analysis ofheteroscedasticity.
