✦ LIBER ✦

On the normal uniform local domain of attraction for intermediate order statistics

✍ Scribed by Johan Segers

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 83 KB
Volume: 53
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(01)00063-3

No coin nor oath required. For personal study only.

✦ Synopsis

Let X1; X2; : : : be independent observations from the absolutely continuous distribution function F with quantile function Q. The density of the normalized order statistic X n-kn+1 : n converges locally uniformly to the standard normal density for any sequence kn with kn → ∞ and kn=n → 0 if and only if log (d=d x)Q(1 -1=x) is slowly oscillating.

📜 SIMILAR VOLUMES

Asymptotics for multivariate t-statistic

Asymptotics for multivariate t-statistic for random vectors in the generalized domain of attraction of the multivariate normal law

✍ Steven J. Sepanski 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 497 KB

A goodness-of-fit test for normality bas

A goodness-of-fit test for normality based on the sample entropy of order statistics

✍ Sangun Park 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 67 KB

The sample entropy, the estimate of the entropy per observation, has been introduced by Vasicek ((1976) A test for normality based on sample entropy, J. Royal Statist. Soc. B 38, 730 -737). In this paper, we provide the sample entropy of order statistics, and present one application of the sample en