LIMIT THEOREMS FOR RANDOM COMPACT SETS IN BANACH SPACE

Chapters in this book

1. I-XII I
2. PREFACE XIII
3. Part I: Time Series and Related Topics
4. LINEAR SERIAL RANK TESTS FOR RANDOMNESS AGAINST ARMA ALTERNATIVES 3
5. LINEAR AND QUADRATIC SERIAL RANK TESTS FOR RANDOMNESS AGAINST SERIAL DEPENDENCE 29
6. LOCALLY ASYMPTOTICALLY OPTIMAL TESTS FOR RANDOMNESS 45
7. OPTIMAL RANK-BASED PROCEDURES FOR TIME SERIES ANALYSIS: TESTING AN ARMA MODEL AGAINST OTHER ARMA MODELS 58
8. ON LOCALLY ASYMPTOTICALLY MAXIMIN TESTS FOR ARMA PROCESSES 89
9. ASYMPTOTICALLY MOST POWERFUL RANK TESTS FOR MULTIVARIATE RANDOMNESS AGAINST SERIAL DEPENDENCE 94
10. WEAK CONVERGENCE OF THE U-STATISTIC AND WEAK INVARIANCE OF THE ONE-SAMPLE RANK ORDER STATISTIC FOR MARKOV PROCESSES AND ARMA MODELS 132
11. WEAK CONVERGENCE OF SERIAL RANK STATISTICS UNDER DEPENDENCE WITH APPLICATIONS IN TIME SERIES AND MARKOV PROCESSES 140
12. ASYMPTOTIC NORMALITY OF L-STATISTICS BASED ON m(n)-DECOMPOSABLE TIME SERIES 167
13. TIME SERIES ANALYSIS VIA RANK ORDER THEORY: SIGNED-RANK TESTS FOR ARMA MODELS 183
14. RANK TESTS FOR TIME SERIES ANALYSIS. A SURVEY 212
15. NONPARAMETRIC PREDICTION FOR RANDOM FIELDS 255
16. ASYMPTOTIC BEHAVIOR OF L-STATISTICS FOR A LARGE CLASS OF TIME SERIES 273
17. ALIGNED RANK TESTS FOR LINEAR MODELS WITH AUTOCORRELATED ERROR TERMS 288
18. CHANGE CURVES IN THE PRESENCE OF DEPENDENT NOISE 351
19. A MULTIVARIATE WALD-WOLFOWITZ RANK TEST AGAINST SERIAL DEPENDENCE 364
20. NONPARAMETRIC APPROACH FOR NON-GAUSSIAN VECTOR STATIONARY PROCESSES 375
21. THE LIMITING DENSITY OF UNIT ROOT TEST STATISTICS: A UNIFYING TECHNIQUE 400
22. Part II: Fuzzy Set Theory and Related Topics
23. INTEGRATION ON FUZZY SETS 415
24. A POSSIBILITY MEASURE IS NOT A FUZZY MEASURE 420
25. STRONG LAW OF LARGE NUMBERS FOR BANACH SPACE VALUED RANDOM SETS 423
26. STRONG LAW OF LARGE NUMBERS WITH RESPECT TO A SET-VALUED PROBABILITY MEASURE 426
27. DIFFERENTIALS OF FUZZY FUNCTIONS 430
28. THE CONCEPT OF NORMALITY FOR FUZZY RANDOM VARIABLES 437
29. LIMIT THEOREMS FOR RANDOM COMPACT SETS IN BANACH SPACE 444
30. FUZZY RANDOM VARIABLES 452
31. GAUSSIAN RANDOM SETS IN BANACH SPACE 466
32. LIMIT THEOREMS FOR FUZZY RANDOM VARIABLES 470
33. CONVERGENCE THEOREM FOR FUZZY MARTINGALES 482
34. LIMIT THEOREMS FOR FUZZY RANDOM VARIABLES 498
35. CENTRAL LIMIT THEOREM FOR BANACH SPACE VALUED FUZZY RANDOM VARIABLES 515
36. STRONG LAW OF LARGE NUMBERS FOR BANACH SPACE VALUED FUZZY RANDOM VARIABLES 524
37. Part III: Miscellaneous Topics
38. LOCAL MAXIMA OF THE SAMPLE FUNCTIONS OF THE Ν -PARAMETER BESSEL PROCESS 535
39. REALIZATION OF lp BY SPACES OF RANDOM VARIABLES 544
40. SHORTED OPERATORS AND GENERALIZED INVERSES OF MATRICES 555
41. COMPLEX PLANAR SPLINES 567
42. SHORTED MATRICES — AN EXTENDED CONCEPT AND SOME APPLICATIONS 587
43. THE FUNDAMENTAL BORDERED MATRIX OF LINEAR ESTIMATION AND THE DUFFIN-MORLEY GENERAL LINEAR ELECTROMECHANICAL SYSTEMS 610
44. COMPLEX CHEBYSHEV POLYNOMIALS AND GENERALIZATIONS WITH AN APPLICATION TO THE OPTIMAL CHOICE OF INTERPOLATING KNOTS IN COMPLEX PLANAR SPLINES 628
45. STRONG SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS FOR MULTIPARAMETER PROCESSES 641
46. A NEW SEMIGROUP TECHNIQUE IN POISSON APPROXIMATION 664
47. INFORMATION 677
48. A LOCAL ALGORITHM FOR CONSTRUCTING NON-NEGATIVE CUBIC SPLINES 696
49. THE TIME SPENT BY THE WIENER PROCESS IN A NARROW TUBE BEFORE LEAVING A WIDE TUBE 712
50. MAXIMUM LIKELIHOOD ESTIMATION FOR STATIONARY POINT PROCESSES 720
51. ON TIME-REVERSIBILITY AND THE UNIQUENESS OF MOVING AVERAGE REPRESENTATIONS FOR NON-GAUSSIAN STATIONARY TIME SERIES 725
52. LOCALLY ASYMPTOTICALLY RANK-BASED PROCEDURES FOR TESTING AUTOREGRESSIVE MOVING AVERAGE DEPENDENCE 727
53. ON SOME LIMIT LAWS FOR PERTURBED EMPIRICAL DISTRIBUTION FUNCTIONS 732
54. Part IV: Appendices A, Β and C 737