Abstract
Let {Xk,k⩾1} be a stationary Gaussian sequence with partial maximum Mn=max {Xk,1⩽k⩽n} and sample mean X̅n=∑k=1nXk/n. Suppose that some of the random variables X1,X2,… can be observed and the others not. Denote by M̃n 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 (M̃n−X̅n,Mn−X̅n).
Citation
Zuoxiang Peng. Ping Wang. Saralees Nadarajah. "Limiting distributions and almost sure limit theorems for the normalized maxima of complete and incomplete samples from Gaussian sequence." Electron. J. Statist. 3 851 - 864, 2009. https://doi.org/10.1214/09-EJS443
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