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An ergodic theorem for proportions of observations that fall into random sets determined by sample quantiles

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  • Anna Dembińska

    (Warsaw University of Technology)

Abstract

Assume that a sequence of observations $$(X_n; n\ge 1)$$ ( X n ; n ≥ 1 ) forms a strictly stationary process with an arbitrary univariate cumulative distribution function. We investigate almost sure asymptotic behavior of proportions of observations in the sample that fall into a random region determined by a given Borel set and a sample quantile. We provide sufficient conditions under which these proportions converge almost surly and describe the law of the limiting random variable.

Suggested Citation

  • Anna Dembińska, 2017. "An ergodic theorem for proportions of observations that fall into random sets determined by sample quantiles," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(3), pages 319-332, April.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:3:d:10.1007_s00184-016-0606-8
    DOI: 10.1007/s00184-016-0606-8
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    References listed on IDEAS

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