Asymptotic behavior of central order statistics from stationary processes

作者：Dembinska Anna^*

来源：Stochastic Processes and Their Applications, 2014, 124(1): 348-372.

DOI：10.1016/j.spa.2013.08.001

• Central order statistics
• Stationary processes
• Linear processes
• Quantiles
• Conditional quantiles
• Almost sure convergence

In this paper, we show that central order statistics from strictly stationary and ergodic sequences are strongly consistent estimators of population quantiles provided that the quantiles are unique. We generalize this result to strictly stationary but not necessarily ergodic sequences. We also describe three types of possible asymptotic behavior of central order statistics in the case when the corresponding population quantile is not unique. We give applications of the presented results to linear processes with both absolutely continuous and discrete innovations.

• 出版日期2014-1