PREFACE
l
LATTICE PATH PROBLEMS AND VECTORS 0F INTEGERS
1. Representation of subsets of {1, ..., N}
2. A refinement of the Chung-Feller Theorem
3. Lattice paths and the ballot theorem
4. Repeated reflections and applications
Exercises
References
II
THE DOMINANCE THEOREM AND SMIRNOV TEST-STATISTICS
l. A theorem on domination and its geometrical interpretation
2. Discussion of the dominance theorem and some special cases
3. Duality and application to Smirnov statistics
Exercises
References
III
SOME APPLICATIONS OF DOMINANCE T0 STATISTICAL PROBLEMS
1. The role of dominance in combinatorial problems
2. Dominance tests for Lehmann alternatives
Exercises
References
IV
THE COMBINATORICS OF KNOCK-OUT TOURNAMENTS
1. The classical case
2. Random knock-out tournaments
3. A comparison of tournaments
Exercises
References
V
A MISCELLANY OF FURTHER RESEARCH PROBLEMS
1. A comparison of selection procedures
2. The numbers {n choose r}{n choose r-1}/n
3. Weak inadmissibility of tests
Exercise
References
APPENDIX
On some convolution identities from lattice path combinatorics
References
NOTES AND SOLUTIONS
SUPPLEMENTARY BIBLIOGRAPHY
INDEX
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