On the extreme order statistics for stationary Gaussian sequences subject to random missing observations

2023/06/24 by Yuan Fang, Fang, Yuan, Zhongquan Tan +1
Computer Science · Economics, Econometrics and Finance · Environmental Science · #60G15 #60G70 #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Hydrology and Drought Analysis #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2306.13861

openalex publication_date 2023/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X=\X_n\_{n≥ 1} be a sequence of stationary Gaussian variables and suppose that only some of the random variables from X can be observed. In this paper, by studying the limiting properties of multidimensional exceedance point processes for X, we derived the joint limit distribution of extreme order statistics for the Gaussian sequence X and its observed ones. The joint limit distribution of the locations and heights of the maxima for the Gaussian sequence X and its observed ones are also obtained.

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