I. S. Borisov, D. I. Sidorov, “Limit theorems for additive statistics based on moving average samples”, Mat. Tr., 2010, Volume 13, Number 2,Pages <nobr>10

Limit theorems for additive statistics based on moving average samples

I. S. Borisov^ab, D. I. Sidorov^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: We study statistics based on samples of moving averages generated by stationary sequence of random variables. The central limit theorem (CLT) is proved for sequences of observations defined by an analytic function of moving averages under consideration. For $U$- and $V$-statistics with canonical (degenerate) kernels, the limit distributions are studied.

Key words: moving averages, central limit theorem, canonical $U$- and $V$-statistics, Hermite polynomials.

UDC: 519.21

Received: 26.04.2010