Probability Theory and Extreme Value Theory (eBook)

I-XII -- Part I Limit Theorems, Rates of Convergence, and Related Topics (Independent Case) -- ORDER OF NORMAL APPROXIMATION FOR RANK TEST STATISTICS DISTRIBUTION -- CONVERGENCE AND REMAINDER TERMS IN LINEAR RANK STATISTICS -- INVARIANCE PRINCIPLES FOR RANK STATISTICS FOR TESTING INDEPENDENCE -- ON THE DEGENERATION OF THE VARIANCE IN THE ASYMPTOTIC NORMALITY OF SIGNED RANK STATISTICS -- ON THE ORDER OF MAGNITUDE OF CUMULANTS OF VON MISES FUNCTIONALS AND RELATED STATISTICS -- ON BERRY-ESSEEN RATES, A LAW OF THE ITERATED LOGARITHM AND AN INVARIANCE PRINCIPLE FOR THE PROPORTION OF THE SAMPLE BELOW THE SAMPLE MEAN -- CRAMÉR TYPE LARGE DEVIATIONS FOR GENERALIZED RANK STATISTICS -- ON THE RATE OF CONVERGENCE IN THE CENTRAL LIMIT THEOREM FOR SIGNED RANK STATISTICS -- A SHARPENING OF THE REMAINDER TERM IN THE HIGHER-DIMENSIONAL CENTRAL LIMIT THEOREM FOR MULTILINEAR RANK STATISTICS -- THE ORDER OF NORMAL APPROXIMATION FOR SIGNED LINEAR RANK STATISTICS -- CENTRAL LIMIT THEOREM FOR PERTURBED EMPIRICAL DISTRIBUTION FUNCTIONS EVALUATED AT A RANDOM POINT -- LIMIT THEOREMS FOR RANDOM CENTRAL ORDER STATISTICS -- ASYMPTOTIC EXPANSIONS FOR SUMS OF NONIDENTICALLY DISTRIBUTED BERNOULLI RANDOM VARIABLES -- ON THE RATE OF CONVERGENCE IN NORMAL APPROXIMATION AND LARGE DEVIATION PROBABILITIES FOR A CLASS OF STATISTICS -- ON HILBERT-SPACE-VALUED U-STATISTICS -- ON THE CENTRAL LIMIT THEOREM IN HILBERT SPACE WITH APPLICATION TO U-STATISTICS -- ASYMPTOTIC EXPANSIONS IN STATISTICS: A REVIEW OF METHODS AND APPLICATIONS -- NORMAL APPROXIMATION OF U-STATISTICS IN HILBERT SPACE -- Part II Limit Theorems (Dependent Case) -- EMPIRICAL DISTRIBUTION FUNCTIONS AND FUNCTIONS OF ORDER STATISTICS FOR MIXING RANDOM VARIABLES -- AN INVARIANCE PRINCIPLE FOR PROCESSES INDEXED BY TWO PARAMETERS AND SOME STATISTICAL APPLICATIONS -- LIMITING BEHAVIOR OF U-STATISTICS, V-STATISTICS, AND ONE SAMPLE RANK ORDER STATISTICS FOR NONSTATIONARY ABSOLUTELY REGULAR PROCESSES -- WEAK INVARIANCE OF GENERALIZED U-STATISTICS FOR NONSTATIONARY ABSOLUTELY REGULAR PROCESSES -- THE SPACE D?k AND WEAK CONVERGENCE FOR THE RECTANGLE-INDEXED PROCESSES UNDER MIXING -- WEAK INVARIANCE OF THE MULTIDIMENSIONAL RANK STATISTIC FOR NONSTATIONARY ABSOLUTELY REGULAR PROCESSES -- WEAK CONVERGENCE OF THE SIMPLE LINEAR RANK STATISTIC UNDER MIXING CONDITIONS IN THE NONSTATIONARY CASE -- WEAK CONVERGENCE OF WEIGHTED EMPIRICAL U-STATISTICS PROCESSES FOR DEPENDENT RANDOM VARIABLES -- LAW OF THE ITERATED LOGARITHM FOR PERTURBED EMPIRICAL DISTRIBUTION FUNCTIONS EVALUATED AT A RANDOM POINT FOR NONSTATIONARY RANDOM VARIABLES -- VALID EDGEWORTH EXPANSIONS OF M-ESTIMATORS IN REGRESSION MODELS WITH WEAKLY DEPENDENT RESIDUALS -- CONDITIONAL U-STATISTICS FOR DEPENDENT RANDOM VARIABLES -- WEAK CONVERGENCE OF SEQUENCES OF FIRST PASSAGE PROCESSES AND APPLICATIONS -- CONDITIONAL EMPIRICAL PROCESSES DEFINED BY NONSTATIONARY ABSOLUTELY REGULAR SEQUENCES -- Part III Extreme Value Theory -- A STRONG INVARIANCE PRINCIPLE CONCERNING THE J-UPPER ORDER STATISTICS FOR STATIONARY m-DEPENDENT SEQUENCES -- A STRONG INVARIANCE PRINCIPLE CONCERNING THE J-UPPER ORDER STATISTICS FOR STATIONARY GAUSSIAN SEQUENCES -- EXTREMES OF MARKOV SEQUENCES -- RECORDS AND 2-BLOCK RECORDS OF 1-DEPENDENT STATIONARY SEQUENCES UNDER LOCAL DEPENDENCE -- Part IV Appendices A, ? and C -- Appendix A Volume 1 Nonparametric Methods in Statistics and Related Topics -- Appendix ? Volume 3 Time Series, Fuzzy Analysis and Miscellaneous Topics -- Appendix C The Publications of Madan Lal Puri