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

Anna Dembińska ()
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Anna Dembińska: Warsaw University of Technology

Metrika: International Journal for Theoretical and Applied Statistics, 2017, vol. 80, issue 3, No 5, 319-332

Abstract: 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.

Keywords: Near order statistic observations; Stationary processes; Quantiles; Conditional quantiles; Almost sure convergence (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00184-016-0606-8

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