Asymptotic distributions of maxima of complete and incomplete samples from multivariate stationary Gaussian sequences

Let (Xn) be a sequence of dd-dimensional stationary Gaussian vectors, and let Mn denote the partial maxima of {Xk,1≤k≤n}. Suppose that there are missing data in each component of Xk and let M˜n denote the partial maxima of the observed variables. In this note, we study two kinds of asymptotic distributions of the random vector (M˜n,Mn) where the correlation and cross-correlation satisfy some dependence conditions.