✦ LIBER ✦
Asymptotic Behavior of the Perturbed Empirical Distribution-Functions Evaluated at a Random Point for Absolutely Regular Sequences
✍ Scribed by S. Sun
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 447 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0047-259X
No coin nor oath required. For personal study only.
✦ Synopsis
Let (\hat{F}{n}) be an estimator obtained by integrating a kernel type density estimator based on a random sample of size (n) from smooth distribution function (F). A central limit theorem is established for the target statistic (\hat{F}{n}\left(U_{n}\right)) where the underlying random variable form an absolutely regular stationary process and where (\left{U_{n}\right}) is a sequence of (U)-statistics. The result obtained generalizes Puri and Ralescu (1986, J. Multivariate Anal. 19, 273-279) under the iid set-up. 1993 Academic Press. Inc.