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

Let ( X n ) be a sequence of d -dimensional stationary Gaussian vectors, and let M n denote the partial maxima of { X k , 1 ≤ k ≤ n } . Suppose that there are missing data in each component of X k 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 , M n ) where the correlation and cross-correlation satisfy some dependence conditions.