Electronic Journal of Statistics

Limiting distributions and almost sure limit theorems for the normalized maxima of complete and incomplete samples from Gaussian sequence

Zuoxiang Peng, Ping Wang, and Saralees Nadarajah

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Abstract

Let {Xk,k1} be a stationary Gaussian sequence with partial maximum Mn=max {Xk,1kn} and sample mean n=k=1nXk/n. Suppose that some of the random variables X1,X2, can be observed and the others not. Denote by n the maximum of the observed random variables from the set {X1,X2,,Xn}. Under some mild conditions, we prove the joint limiting distribution and the almost sure limit theorem for (nn,Mnn).

Article information

Source
Electron. J. Statist., Volume 3 (2009), 851-864.

Dates
First available in Project Euclid: 21 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1250880018

Digital Object Identifier
doi:10.1214/09-EJS443

Mathematical Reviews number (MathSciNet)
MR2534204

Zentralblatt MATH identifier
1326.62040

Subjects
Primary: 62F15: Bayesian inference
Secondary: 60G70: Extreme value theory; extremal processes 60F15: Strong theorems

Keywords
Almost sure limit theorem complete and incomplete samples limiting distribution maximum stationary Gaussian sequence

Citation

Peng, Zuoxiang; Wang, Ping; Nadarajah, Saralees. Limiting distributions and almost sure limit theorems for the normalized maxima of complete and incomplete samples from Gaussian sequence. Electron. J. Statist. 3 (2009), 851--864. doi:10.1214/09-EJS443. https://projecteuclid.org/euclid.ejs/1250880018


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