Complete Convergence for Weighted Sums of Arrays of Random Elements
نویسنده
چکیده
Let {Xnk: k,n 1,2 be an array of row-wise independent random elements in a separable Banach space. Let {ank: k,n 1,2 be an array of Voo voo R+ real numbers such that /-k=l lank -< 1 and Ln=l exp(-a/A < for each c e where n V 2 Voo An kk=l ank. The complete convergence of l’k=l ank Xnk is obtained under varying moment and distribution conditions on the random elements. In particular, laws of large numbers follow for triangular arrays of random elements, and consistency of the kernel density estimates is obtained from these results.
منابع مشابه
Complete Convergence and Some Maximal Inequalities for Weighted Sums of Random Variables
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