Probability and Statistical Models with Applications
By: CH. A. Charalambides (Editor), M.V. Koutras (Editor), N. Balakrishnan (Editor)
Hardcover | 21 September 2000 | Edition Number 1
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666 Pages
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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 |
Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9781584881247
ISBN-10: 1584881240
Published: 21st September 2000
Format: Hardcover
Language: English
Number of Pages: 666
Audience: General Adult
Publisher: Taylor & Francis Ltd
Country of Publication: US
Edition Number: 1
Dimensions (cm): 23.39 x 15.6 x 3.66
Weight (kg): 1.1
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