Maxima and minima of complete and incomplete stationary sequences

In the seminal contribution [R.A. Davis, Maxima and minima of stationary sequences, Ann. Probab. 7(3) (1979), pp. 453–460.] 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 the minima of both complete and incomplete samples. It turns out that the maxima and the minima are asymptotically independent when is a deterministic constant.