THE ASYMPTOTIC DEPENDENCE STRUCTURE AND SOME FUNCTIONS OF GENERALIZED ORDER STATISTICS IN A STATIONARY GAUSSIAN SEQUENCE

The main aim of this paper is to study the limit joint distribution function (df) of any two extreme, as well as central, m-generalized order statistics (m-gos) of a stationary Gaussian sequence under an equi-correlated set-up. It is shown that under this general set-up, any lower and upper extremes are asymptotically dependent unless the correlation is of order omicron(1/log n); on the contrary of gos based on i.i.d random variables (rv's). Moreover, under this general framework of study, the classes of possible non-degenerate limit df's of the generalized quasiranges, quasi-mid-ranges, extremal quotient, extremal product and the ratio of the symmetric differences of m-gos are obtained. It is worth mentioning that, the results of this paper contribute not only to a critical assessment of existing statistical methodology, but also help to address their limitations within different contexts