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This monograph extends the notion of locally most powerful rank
tests to non-regular cases. Through this no- tion one is led in a
natural way to "non-standard" rank tests. A nearly complete
analysis of the finite sample and asymptotic properties of such
rank tests is presented. Also an adaptive test procedure is
proposed and studied, and the results of a Monte Carlo simulation
are given which provide strong evidence that it should perform well
in many practical situations. An appendix derives the limit
experiments needed to investigate the asymptotic optimality of
these "non-standard" rank tests under local alternatives. The
results in the appendix should also be of separate interest.
This book is intended to give an account of the theory of infi
nitely divisible statistical experiments which started from LeCam,
1974. It includes a presentation of LeCam's basic results as well
as new developments in the field. The book consists of four
chapters written by different authors. Chapters I, III and IV have
been prepared in Bayreuth with the support of the Deutsche
Forschungsgemeinschaft (DFG); Chapter II is part of its author's
Habilitationsschrift, 1982 (Dortmund). For the reader's
convenience, the chapters have been unified in presentation,
without neglecting differences in the individual styles of writing.
The authors are grateful to Dr. C. Becker for carefully reviewing
the manuscript. Furthermore, acknowledgements are gratefully
extended to the DFG for partly subsidizing Dr. Becker and the
second author by a grant. Some special words of thanks are due to
Mrs. Witzigmann, who typed the final manuscript and its
predecessors with patience and skill. Universitat Bayreuth und A.
Janssen Universitat Dortmund, H. Milbrodt Dezember 1984 H. Strasser
CONTENTS Preface Introduction L its of Triangular Arrays of 14 I.
EXEeriments (H. Milbrodt and H. Strasser) 1. Basic Concepts 14 19
2. Gaussian Exper ents 3. Introduction to Poisson Experiments 25 4.
Convergence of Poisson Experiments 32 5. Convergence of Triangular
Arrays 38 6. Identification of Limit Experiments 47 The
Levy-Khintchine Formula for Infinitely 55 II."
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