Jaroslav Hájek and asymptotic theory of rank tests

In the series of papers [1-3,5,6,8,9,11,12] (papers [11] and [12] were written joint­ ly with V. Dupac), Hajek systematically investigated the asymptotic properties of linear rank statistics under null hypotheses, under local (contiguous) and some non­ local alternatives. Besides that , in [4] he derived the rank test of independence in a bivariate distribution, locally most powerful against specific dependence alterna­ tives. T h e results published before 1967 were then included, unified and elaborated, in the monograph [10], written jointly with Z. Sidak. Hajek's textbook [7] of rank tests also deserves your attention. This collection of papers, though not of a great size, represents a substantial contribution to the asymptotic theory of rank tests; it was a starting point of a research of many authors and it is a rich source of ideas even today. Each of these papers not only brings new original results, but these results are proved by new, original methods which were later frequently used also in many other contexts. Let us briefly characterize the main Hajek's asymptotic results on rank tests.