Joint Limiting Distribution of Minima and Maxima of Complete and Incomplete Samples of Stationary Sequences

Abstract

In the seminal contribution [4] the joint weak convergence of maxima and minima of weakly dependent stationary sequences is derived under some mild asymptotic conditions. In this paper we address additionally the case of incomplete samples assuming that the average proportion of incompleteness converges in probability to some random variable. We show the joint weak convergence of the maxima and minima of both complete and incomplete samples. It turns out that for special cases, maxima and minima are asymptotically independent.