The death of Jaroslav Hajek on June 10, 1974 was a heavy loss to many mathe- maticians all around the world. The impact of his work on mathematical statistics has been so extraordinary that it has completely changed the character of some fields of this science. Some of his ideas have become a part of the common statistical conSClOusness. Hajek's contribution to statistics includes research in the theory of rank tests, parametric estimation, probability sampling, statistical inference in stochastic processes and various other specializations. His results were always of fundamental character for the corresponding field and they continue to stimulate further research and progress. For proving the results, he developed original methods which are now commonly used for the solution of many related problems. Hajek was an enthusiastic mathematician; the secret of his success was in his love for the subject and in his great sense for practical applications; just practical problems provided him the source of excellent mathematical problems and ideas. We see the best way of commemorating Jaroslav Hajek in the arrangement of the present volume which collects papers of authors whose work is related to Hajek's work and who were friends of him. The authors come from Czechoslovakia, Hungary. the Netherlands, Sweden, U.S.A .. U.S.S.R., and West Germany. I wish to thank most cordially all the authors and all who contributed in any way to the success of the publication.