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

作者：Dembinska Anna

来源：Metrika, 2017, 80(3): 319-332.

DOI：10.1007/s00184-016-0606-8

• Near order statistic observations
• Stationary processes
• Quantiles
• Conditional quantiles
• Almost sure convergence

Assume that a sequence of observations 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.

• 出版日期2017-4