Limit distribution of maxima of strongly dependent Gaussian vector sequences under complete and incomplete samples

Let {Xn,n≥1} be a sequence of d-dimensional stationary Gaussian vectors, and let Mn denote the maxima of {Xk,1≤k≤n}. Suppose that there are missing data in each component of Xk and let M˜n denote the maxima of the observed variables. In this paper, we study the asymptotic distribution of the random vector (M˜n,Mn) as the correlation and cross-correlation satisfy strongly dependent conditions.