Rank Tests with Estimated Scores and Their Application

The general aim of this book is to present a new class of nonlinear rank tests for a variety of important testing problems. The need for such new procedures sterns from the fact that the classical linear rank tests
are sensitive only for small classes of alternatives, while our nonlinear rank tests are designed to be sensitive for broad classes of alternatives. The development of the new proce dures is strongly influenced by the opinion
that in many real world situations the classical shift assumption is too idealized. By introducing general nonpara metrie models we get rid of the shift assumption. For the two-sample situation a detailed motivation is given
in Chapter l. Our theoretical results and many Monte Carlo simulations have convinced us that the proposed procedures are of real practical importance and should be used in statistical applications. Therefore in Chapter 2 we
present a simple algorithmic description of the new rank tests-without stressing any mathe matical theory-and a step by step evaluation of numerical examples, whereas in Part 11 of the book (Chapters 2-6) we give a rigorous
asymptotic theory of all proposals of Chapter 2. These chapters discuss different models and motivate the special proposals. Most of the concepts and of the theoretical results are based on our own work.