Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series A, Pt. 2, pp. 194--205

CONVERGENCE RATES IN r-MEAN AND IN THE LAW OF LARGE NUMBERS FOR DRCE RANDOM ARRAY

By

DING KEYUE, Wuhan Institute of Mathematical Sciences

SUMMARY.  Let Xi, Yj, and Vi,j be independent families of i.i.d. random variables, uniformly distributed on [0,1]. For any Borel function defined on $[0,1]_3$, ${f(X_{i}, Y_{j}, V_{i,j})}_{i \geq1, j \geq 1} is called DRCE random array. Under certain moment conditions on f, we obtain that $\sum_{m=1}^{\infty} \sum_{n=1}^{\infty}(mn)_{\alpha r-2} P(|S_{m,n}| \geq \epsilon (mn)^{\alpha}) < \infty$, for $0 \leq r <2, \sum_{m=1}^{\infty} \sum_{n=1}^{\infty}(mn)_{r-2} P(|S_{m,n}| \geq \epsilon mn) < \infty$ for $r \leq 2$; at the same time, we get the convergence rates of Sm, n in r-mean, $r \leq 1$, where Smn=$\sum_{i=1}^{m} \sum_{j=1}^{n} f(X_i, Y_j, V_{i,j})$.

AMS (1990) subject classification.  60F15,60F10, 60G09.

Key words and phrases. Convergence rate, law of large number, row-column exchangeable.

Full paper (PDF)

This article in Mathematical Reviews.