| Preface | p. v |
| List of Contributors | p. xix |
| List of Tables | p. xxv |
| List of Figures | p. xxvii |
| Theophilos N. Cacoullos--A View of his Career | p. xxxix |
| Publications of Theophilos N. Cacoullos | p. xxxii |
| The Ten Commandments for a Statistician | p. xxxviii |
| Approximation, Bounds, and Inequalities | |
| Nonuniform Bounds in Probability Approximations Using Stein's Method | p. 3 |
| Introduction | p. 3 |
| Poisson Approximation | p. 4 |
| Binomial Approximation: Binary Expansion of a Random Integer | p. 7 |
| Normal Approximation | p. 9 |
| Conclusion | p. 11 |
| References | p. 11 |
| Probability Inequalities for Multivariate Distributions with Applications to Statistics | p. 15 |
| Introduction and Summary | p. 15 |
| Positive Dependence and Product-Type Inequalities | p. 17 |
| Negative Dependence and Product-Type Inequalities | p. 22 |
| Bonferroni-Type Inequalities | p. 23 |
| Applications | p. 27 |
| References | p. 37 |
| Applications of Compound Poisson Approximation | p. 41 |
| Introduction | p. 41 |
| First Applications | p. 45 |
| Word Counts | p. 50 |
| Discussion and Numerical Examples | p. 58 |
| References | p. 60 |
| Compound Poisson Approximation for Sums of Dependent Random Variables | p. 63 |
| Introduction | p. 63 |
| Preliminaries and Notations | p. 66 |
| Main Results | p. 67 |
| Examples of Applications | p. 76 |
| References | p. 85 |
| Unified Variance Bounds and a Stein-Type Identity | p. 87 |
| Introduction | p. 87 |
| Properties of the Transformation | p. 89 |
| Application to Variance Bounds | p. 94 |
| References | p. 98 |
| Probability Inequalities for U-Statistics | p. 101 |
| Introduction | p. 101 |
| Preliminaries | p. 103 |
| Probability Inequalities | p. 106 |
| References | p. 112 |
| Probability and Stochastic Processes | |
| Theory and Applications of Decoupling | p. 117 |
| Complete Decoupling of Marginal Laws and One-Sided Bounds | p. 118 |
| Tangent Sequences and Conditionally Independent Variables | p. 123 |
| Basic Decoupling Inequalities for Tangent Sequences | p. 124 |
| Applications to Martingale Inequalities and Exponential Tail Probability Bounds | p. 128 |
| Decoupling of Multilinear Forms, U-Statistics and U-Processes | p. 130 |
| Total Decoupling of Stopping Times | p. 134 |
| Principle of Conditioning in Weak Convergence | p. 139 |
| Conclusion | p. 141 |
| References | p. 142 |
| A Note on the Probability of Rapid Extinction of Alleles in a Wright-Fisher Process | p. 147 |
| Introduction | p. 147 |
| The Lower Bound for Boundary Sets | p. 150 |
| References | p. 154 |
| Stochastic Integral Functionals in an Asymptotic Split State Space | p. 155 |
| Introduction | p. 155 |
| Preliminaries | p. 156 |
| Phase Merging Scheme for Markov Jump Processes | p. 159 |
| Average of Stochastic Integral Functional | p. 160 |
| Diffusion Approximation of Stochastic Integral Functional | p. 161 |
| Integral Functional with Perturbed Kernel | p. 166 |
| References | p. 167 |
| Busy Periods for Some Queues with Deterministic Interarrival or Service Times | p. 169 |
| Introduction | p. 169 |
| Preliminaries: A Basic Class of Polynomials | p. 171 |
| The D[subscript g]/M[superscript (Q)]/1 Queue | p. 174 |
| The M[superscript (Q)]/D[subscript g]/1 Queue | p. 179 |
| References | p. 183 |
| The Evolution of Population Structure of the Perturbed Non-Homogeneous Semi-Markov System | p. 185 |
| Introduction | p. 185 |
| The Perturbed Non-Homogeneous Semi-Markov System | p. 187 |
| The Expected Population Structure with Respect to the First Passage Time Probabilities | p. 190 |
| The Expected Population Structure with Respect to the Duration of a Membership in a State | p. 196 |
| The Expected Population Structure with Respect to the State Occupancy of a Membership | p. 199 |
| The Expected Population Structure with Respect to the Counting Transition Probabilities | p. 201 |
| References | p. 203 |
| Distributions, Characterizations, and Applications | |
| Characterizations of Some Exponential Families Based on Survival Distributions and Moments | p. 209 |
| Introduction | p. 209 |
| An Auxiliary Lemma | p. 211 |
| Characterizations Based on Survival Distributions | p. 212 |
| Characterizations Based on Moments | p. 218 |
| References | p. 222 |
| Bivariate Distributions Compatible or Nearly Compatible with Given Conditional Information | p. 225 |
| Introduction | p. 225 |
| Imprecise Specification | p. 226 |
| Precise Specification | p. 228 |
| An Example | p. 233 |
| References | p. 237 |
| A Characterization of a Distribution Arising from Absorption Sampling | p. 239 |
| Introduction | p. 239 |
| The Characterization Theorem | p. 242 |
| An Application | p. 244 |
| References | p. 245 |
| Refinements of Inequalities for Symmetric Functions | p. 247 |
| References | p. 250 |
| General Occupancy Distributions | p. 253 |
| Introduction | p. 253 |
| A General Random Occupancy Model | p. 255 |
| Special Occupancy Distributions | p. 260 |
| References | p. 268 |
| A Skew t Distribution | p. 269 |
| Introduction | p. 269 |
| Derivation of Skew t Density | p. 270 |
| Properties of Skew t Distribution | p. 272 |
| A First Bivariate Skew t Distribution | p. 274 |
| A Second Bivariate Skew t Distribution | p. 275 |
| References | p. 277 |
| On the Posterior Moments for Truncation Parameter Distributions and Identifiability by Posterior Mean for Exponential Distribution with Location Parameters | p. 279 |
| Introduction | p. 279 |
| Posterior Moments | p. 281 |
| Examples | p. 286 |
| Identifiability by Posterior Mean | p. 287 |
| An Illustrative Example | p. 289 |
| References | p. 289 |
| Distributions of Random Volumes without Using Integral Geometry Techniques | p. 293 |
| Introduction | p. 294 |
| Evaluation of Arbitrary Moments of the Random Volumes | p. 299 |
| References | p. 316 |
| Time Series, Linear, and Non-Linear Models | |
| Cointegration of Economic Time Series | p. 319 |
| Introduction | p. 319 |
| Regression Models | p. 320 |
| Simultaneous Equation Models | p. 321 |
| Canonical Analysis and the Reduced Rank Regression Estimator | p. 323 |
| Autoregressive Processes | p. 325 |
| Nonstationary Models | p. 326 |
| Cointegrated Models | p. 327 |
| Asymptotic Distribution of Estimators and Test Criterion | p. 328 |
| References | p. 331 |
| On Some Power Properties of Goodness-of-Fit Tests in Time Series Analysis | p. 333 |
| Testing Spectral Density Fits | p. 333 |
| Local Power Considerations | p. 337 |
| Comparison | p. 340 |
| References | p. 348 |
| Linear Constraints on a Linear Model | p. 349 |
| Introduction | p. 349 |
| Geometric Interpretation of the Role of the Linear Constraints | p. 351 |
| References | p. 357 |
| M-Methods in Generalized Nonlinear Models | p. 359 |
| Introduction | p. 359 |
| Definitions and Assumptions | p. 361 |
| Asymptotic Results | p. 363 |
| Test of Significance and Computational Algorithm | p. 371 |
| References | p. 373 |
| Inference and Applications | |
| Extensions of a Variation of the Isoperimetric Problem | p. 379 |
| Introduction | p. 379 |
| Information Retrieval Problem | p. 380 |
| Information Retrieval without Measurement Error | p. 381 |
| Useful Information in a Variable | p. 382 |
| Allocation of Storage Space | p. 383 |
| The Isoperimetric Problem | p. 383 |
| Extensions | p. 384 |
| References | p. 387 |
| On Finding a Single Positive Unit in Group Testing | p. 391 |
| Introduction | p. 391 |
| Description of Properties, Numerical Results | p. 392 |
| Some Formulas for Procedure R[subscript DH] | p. 396 |
| The Greedy Procedure R[subscript G] | p. 398 |
| Conclusions | p. 398 |
| Changing the Prior with Procedure R[subscript DH] | p. 399 |
| Robustness of Procedure R[subscript DH] for q Known | p. 400 |
| References | p. 401 |
| Testing Hypotheses on Variances in the Presence of Correlations | p. 403 |
| Bivariate Normal Population | p. 403 |
| Modifying the Hypothesis | p. 406 |
| Nonnull Moments | p. 408 |
| Null Case | p. 413 |
| The Conditional Hypothesis | p. 415 |
| References | p. 418 |
| Estimating the Smallest Scale Parameter: Universal Domination Results | p. 419 |
| Introduction | p. 419 |
| Main Results | p. 420 |
| References | p. 426 |
| On Sensitivity of Exponential Rate of Convergence for the Maximum Likelihood Estimator | p. 429 |
| Introduction | p. 429 |
| Main Results | p. 431 |
| Some Applications | p. 436 |
| Discussion | p. 442 |
| References | p. 443 |
| A Closer Look at Weighted Likelihood in the Context of Mixtures | p. 447 |
| Introduction | p. 447 |
| Background | p. 449 |
| Simulation Experiments and Results | p. 452 |
| Model Selection | p. 464 |
| Conclusions | p. 465 |
| References | p. 465 |
| On Nonparametric Function Estimation with Infinite-Order Flat-Top Kernels | p. 469 |
| Introduction: A General Family of Flat-Top Kernels of Infinite Order | p. 469 |
| Multivariate Density Estimation: A Review | p. 472 |
| Further Issues on Density Estimation | p. 475 |
| References | p. 481 |
| Multipolishing Large Two-Way Tables | p. 485 |
| Introduction | p. 485 |
| Bilinear Multipolishers | p. 486 |
| Matrix Approximations | p. 489 |
| Displays | p. 492 |
| Example | p. 493 |
| Concluding Remarks | p. 495 |
| References | p. 496 |
| On Distances and Measures of Information: A Case of Diversity | p. 503 |
| Introduction | p. 503 |
| Measuring Information--Measures of Information | p. 505 |
| Properties of Measures of Information | p. 508 |
| Measures of Information and Inference | p. 509 |
| Applications | p. 511 |
| Conclusions | p. 512 |
| References | p. 512 |
| Representation Formulae for Probabilities of Correct Classification | p. 517 |
| Introduction | p. 517 |
| Vector Algebraic Preliminaries | p. 519 |
| Distributional Results | p. 525 |
| References | p. 534 |
| Estimation of Cycling Effect on Reliability | p. 537 |
| Models | p. 537 |
| Semiparametric Estimation | p. 539 |
| References | p. 544 |
| Applications to Biology and Medicine | |
| A New Test for Treatment vs. Control in an Ordered 2 [times] 3 Contingency Table | p. 549 |
| Introduction | p. 549 |
| New Test, Implementation and Example | p. 551 |
| Simulation Study | p. 553 |
| Theoretical Properties | p. 554 |
| Appendix | p. 559 |
| References | p. 563 |
| An Experimental Study of the Occurrence Times of Rare Species | p. 565 |
| Statement of the Problem | p. 565 |
| The Design of the Experiment | p. 566 |
| Stage 2 of the Experiment | p. 568 |
| Findings | p. 569 |
| References | p. 571 |
| A Distribution Functional Arising in Epidemic Control | p. 573 |
| Introduction | p. 573 |
| Properties of the Functional | p. 574 |
| Proof of the Theorem | p. 577 |
| Application to Epidemic Control | p. 579 |
| References | p. 581 |
| Birth and Death Urn for Ternary Outcomes: Stochastic Processes Applied to Urn Models | p. 583 |
| Introduction | p. 583 |
| A Birth and Death Urn with Immigration for Ternary Outcomes | p. 584 |
| Embedding the Urn Scheme in a Continuous-Time Birth and Death Process | p. 586 |
| The Probability Generating Function for the Number of Success on Treatment i in the Continuous-Time Birth and Death Process | p. 587 |
| The Probability Generating Function for the Number of Trials on Treatment i in the Continuous-Time Birth and Death Process | p. 590 |
| The Number of Trials on Treatment i in the Continuous-Time Birth and Death Process | p. 591 |
| The Joint Probability Generating Function for the Number of Successes and the Number of Trials in the Continuous-Time Birth and Death Process | p. 593 |
| Adopting a Stopping Rule to Convert Continuous-Time Statistics to the Urn Design | p. 594 |
| Limiting Results for the Proportion of Trials on Treatment i | p. 596 |
| Limiting Results for the Proportion of Successes on Treatment i in the Urn | p. 597 |
| Asymptotic Inference Pertaining to the Success Probabilities | p. 598 |
| Concluding Remarks | p. 599 |
| References | p. 600 |
| Author Index | p. 601 |
| Subject Index | p. 611 |
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