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

摘要

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