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Limit theorems for additive statistics based on moving average samples

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.

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Correspondence to I. S. Borisov.

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Original Russian Text © I. S. Borisov and D. I. Sidorov, 2010, published in Matematicheskie Trudy, 2010, Vol. 13, No. 2, pp. 10–32.

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Borisov, I.S., Sidorov, D.I. Limit theorems for additive statistics based on moving average samples. Sib. Adv. Math. 21, 233–249 (2011). https://doi.org/10.3103/S1055134411040018

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Keywords

  • moving averages
  • central limit theorem
  • canonical U- and V -statistics
  • Hermite polynomials