Supported by National Natural Science Foundation of China (Grant No. 70371061) and the Program for Excellent Talents in Chongqing Higher Education Institutions (Grant No. 120060-20600204)Acknowledgements The authors would like to express their deep thanks to the referees for carefully reading the paper and for their comments which greatly improve the paper.
Let Mn denote the partial maximum of a strictly stationary sequence (Xn). Suppose some of the random variables of (Xn) can be observed and let Mn stand for the maximum of observed random variables from the set {X1...