CONDITIONAL U-STATISTICS FOR DEPENDENT RANDOM VARIABLES

Kapitel in diesem Buch

1. I-XII I
2. Part I Limit Theorems, Rates of Convergence, and Related Topics (Independent Case)
3. ORDER OF NORMAL APPROXIMATION FOR RANK TEST STATISTICS DISTRIBUTION 3
4. CONVERGENCE AND REMAINDER TERMS IN LINEAR RANK STATISTICS 11
5. INVARIANCE PRINCIPLES FOR RANK STATISTICS FOR TESTING INDEPENDENCE 21
6. ON THE DEGENERATION OF THE VARIANCE IN THE ASYMPTOTIC NORMALITY OF SIGNED RANK STATISTICS 37
7. ON THE ORDER OF MAGNITUDE OF CUMULANTS OF VON MISES FUNCTIONALS AND RELATED STATISTICS 54
8. ON BERRY-ESSEEN RATES, A LAW OF THE ITERATED LOGARITHM AND AN INVARIANCE PRINCIPLE FOR THE PROPORTION OF THE SAMPLE BELOW THE SAMPLE MEAN 63
9. CRAMÉR TYPE LARGE DEVIATIONS FOR GENERALIZED RANK STATISTICS 80
10. ON THE RATE OF CONVERGENCE IN THE CENTRAL LIMIT THEOREM FOR SIGNED RANK STATISTICS 91
11. A SHARPENING OF THE REMAINDER TERM IN THE HIGHER-DIMENSIONAL CENTRAL LIMIT THEOREM FOR MULTILINEAR RANK STATISTICS 120
12. THE ORDER OF NORMAL APPROXIMATION FOR SIGNED LINEAR RANK STATISTICS 140
13. CENTRAL LIMIT THEOREM FOR PERTURBED EMPIRICAL DISTRIBUTION FUNCTIONS EVALUATED AT A RANDOM POINT 147
14. LIMIT THEOREMS FOR RANDOM CENTRAL ORDER STATISTICS 154
15. ASYMPTOTIC EXPANSIONS FOR SUMS OF NONIDENTICALLY DISTRIBUTED BERNOULLI RANDOM VARIABLES 183
16. ON THE RATE OF CONVERGENCE IN NORMAL APPROXIMATION AND LARGE DEVIATION PROBABILITIES FOR A CLASS OF STATISTICS 205
17. ON HILBERT-SPACE-VALUED U-STATISTICS 221
18. ON THE CENTRAL LIMIT THEOREM IN HILBERT SPACE WITH APPLICATION TO U-STATISTICS 224
19. ASYMPTOTIC EXPANSIONS IN STATISTICS: A REVIEW OF METHODS AND APPLICATIONS 231
20. NORMAL APPROXIMATION OF U-STATISTICS IN HILBERT SPACE 266
21. Part II Limit Theorems (Dependent Case)
22. EMPIRICAL DISTRIBUTION FUNCTIONS AND FUNCTIONS OF ORDER STATISTICS FOR MIXING RANDOM VARIABLES 289
23. AN INVARIANCE PRINCIPLE FOR PROCESSES INDEXED BY TWO PARAMETERS AND SOME STATISTICAL APPLICATIONS 310
24. LIMITING BEHAVIOR OF U-STATISTICS, V-STATISTICS, AND ONE SAMPLE RANK ORDER STATISTICS FOR NONSTATIONARY ABSOLUTELY REGULAR PROCESSES 362
25. WEAK INVARIANCE OF GENERALIZED U-STATISTICS FOR NONSTATIONARY ABSOLUTELY REGULAR PROCESSES 386
26. THE SPACE D̃k AND WEAK CONVERGENCE FOR THE RECTANGLE-INDEXED PROCESSES UNDER MIXING 406
27. WEAK INVARIANCE OF THE MULTIDIMENSIONAL RANK STATISTIC FOR NONSTATIONARY ABSOLUTELY REGULAR PROCESSES 438
28. WEAK CONVERGENCE OF THE SIMPLE LINEAR RANK STATISTIC UNDER MIXING CONDITIONS IN THE NONSTATIONARY CASE 456
29. WEAK CONVERGENCE OF WEIGHTED EMPIRICAL U-STATISTICS PROCESSES FOR DEPENDENT RANDOM VARIABLES 474
30. LAW OF THE ITERATED LOGARITHM FOR PERTURBED EMPIRICAL DISTRIBUTION FUNCTIONS EVALUATED AT A RANDOM POINT FOR NONSTATIONARY RANDOM VARIABLES 492
31. VALID EDGEWORTH EXPANSIONS OF M-ESTIMATORS IN REGRESSION MODELS WITH WEAKLY DEPENDENT RESIDUALS 517
32. CONDITIONAL U-STATISTICS FOR DEPENDENT RANDOM VARIABLES 533
33. WEAK CONVERGENCE OF SEQUENCES OF FIRST PASSAGE PROCESSES AND APPLICATIONS 550
34. CONDITIONAL EMPIRICAL PROCESSES DEFINED BY NONSTATIONARY ABSOLUTELY REGULAR SEQUENCES 569
35. Part III Extreme Value Theory
36. A STRONG INVARIANCE PRINCIPLE CONCERNING THE J-UPPER ORDER STATISTICS FOR STATIONARY m-DEPENDENT SEQUENCES 607
37. A STRONG INVARIANCE PRINCIPLE CONCERNING THE J-UPPER ORDER STATISTICS FOR STATIONARY GAUSSIAN SEQUENCES 616
38. EXTREMES OF MARKOV SEQUENCES 666
39. RECORDS AND 2-BLOCK RECORDS OF 1-DEPENDENT STATIONARY SEQUENCES UNDER LOCAL DEPENDENCE 683
40. Part IV Appendices A, Β and C
41. Appendix A Volume 1 Nonparametric Methods in Statistics and Related Topics 709
42. Appendix Β Volume 3 Time Series, Fuzzy Analysis and Miscellaneous Topics 715
43. Appendix C The Publications of Madan Lal Puri 721