کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1155833 | 958775 | 2012 | 21 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: UU-processes, UU-quantile processes and generalized linear statistics of dependent data UU-processes, UU-quantile processes and generalized linear statistics of dependent data](/preview/png/1155833.png)
Generalized linear statistics are a unifying class that contains UU-statistics, UU-quantiles, LL-statistics as well as trimmed and Winsorized UU-statistics. For example, many commonly used estimators of scale fall into this class. GLGL-statistics have only been studied under independence; in this paper, we develop an asymptotic theory for GLGL-statistics of sequences which are strongly mixing or L1L1 near epoch dependent on an absolutely regular process. For this purpose, we prove an almost sure approximation of the empiricalUU-process by a Gaussian process. With the help of a generalized Bahadur representation, it follows that such a strong invariance principle also holds for the empirical UU-quantile process and consequently for GLGL-statistics. We obtain central limit theorems and laws of the iterated logarithm for UU-processes, UU-quantile processes and GLGL-statistics as straightforward corollaries.
Journal: Stochastic Processes and their Applications - Volume 122, Issue 3, March 2012, Pages 787–807