Sequential Methods and Their Applications

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ISBN: 9781584881025 | 158488102X
Cover: Hardcover
Copyright: 10/28/2008

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"Taking an accessible, nonmathematical approach to this field, Sequential Methods and Their Applications illustrates the efficiency of sequential methodologies when dealing with contemporary statistical challenges in many areas." "The book first explores fixed sample size, sequential probability ratio, and nonparametric tests. It then presents numerous multistage estimation methods for fixed-width confidence interval as well as minimum and bounded risk problems. The book also describes multistage fixed-size confidence region methodologies, selection methodologies, and Bayesian estimation. Through diverse applications, each chapter provides valuable approaches for performing statistical experiments and facilitating real data analysis."--BOOK JACKET.

Objectives, Coverage, and Hopes	p. 1
Introduction	p. 1
Back to the Origin	p. 1
Recent Upturn and Positive Feelings	p. 2
The Objectives	p. 3
The Coverage	p. 3
Aims and Scope	p. 9
Final Thoughts	p. 11
Why Sequential?	p. 13
Introduction	p. 13
Tests of Hypotheses	p. 13
Estimation Problems	p. 15
Selection and Ranking Problems	p. 17
Computer Programs	p. 20
Exercises	p. 25
Sequential Probability Ratio Test	p. 33
Introduction	p. 33
Termination and Determination of A and B	p. 34
ASN Function and OC Function	p. 41
Examples and Implementation	p. 44
Auxiliary Results	p. 51
Exercises	p. 52
Sequential Tests for Composite Hypotheses	p. 59
Introduction	p. 59
Test for the Variance	p. 59
Test for the Mean	p. 63
Test for the Correlation Coefficient	p. 66
Test for the Gamma Shape Parameter	p. 69
Two-Sample Problem: Comparing the Means	p. 70
Auxiliary Results	p. 71
Exercises	p. 72
Sequential Nonparametric Tests	p. 79
Introduction	p. 79
A Test for the Mean: Known Variance	p. 80
A Test for the Mean: Unknown Variance	p. 82
A Test for the Percentile	p. 83
A Sign Test	p. 84
Data Analyses and Conclusions	p. 85
Exercises	p. 92
Estimation of the Mean of a Normal Population	p. 97
Introduction	p. 97
Fixed-Width Confidence Intervals	p. 98
Bounded Risk Point Estimation	p. 132
Minimum Risk Point Estimation	p. 144
Some Selected Derivations	p. 154
Exercises	p. 161
Location Estimation: Negative Exponential Distribution	p. 165
Introduction	p. 165
Fixed-Width Confidence Intervals	p. 166
Minimum Risk Point Estimation	p. 178
Selected Derivations	p. 189
Exercises	p. 191
Point Estimation of Mean of an Exponential Population	p. 195
Introduction	p. 195
Minimum Risk Estimation	p. 196
Bounded Risk Estimation	p. 200
Data Analyses and Conclusions	p. 204
Other Selected Multistage Procedures	p. 208
Some Selected Derivations	p. 211
Exercises	p. 219
Fixed-Width Intervals from MLEs	p. 223
Introduction	p. 223
General Sequential Approach	p. 223
General Accelerated Sequential Approach	p. 227
Examples	p. 228
Data Analyses and Conclusions	p. 233
Some Selected Derivations	p. 237
Exercises	p. 239
Distribution-Free Methods in Estimation	p. 245
Introduction	p. 245
Fixed-Width Confidence Intervals for the Mean	p. 246
Minimum Risk Point Estimation for the Mean	p. 251
Bounded Length Confidence Interval for the Median	p. 256
Data Analyses and Conclusions	p. 258
Other Selected Multistage Procedures	p. 262
Some Selected Derivations	p. 263
Exercises	p. 269
Multivariate Normal Mean Vector Estimation	p. 277
Introduction	p. 277
Fixed-Size Confidence Region: [Sigma] = [sigma superscript 2]H	p. 278
Fixed-Size Confidence Region: Unknown Dispersion Matrix	p. 284
Minimum Risk Point Estimation: Unknown Dispersion Matrix	p. 289
Data Analyses and Conclusions	p. 293
Other Selected Multistage Procedures	p. 298
Some Selected Derivations	p. 299
Exercises	p. 308
Estimation in a Linear Model	p. 313
Introduction	p. 313
Fixed-Size Confidence Region	p. 315
Minimum Risk Point Estimation	p. 322
Data Analyses and Conclusions	p. 324
Other Selected Multistage Procedures	p. 330
Some Selected Derivations	p. 331
Exercises	p. 334
Estimating the Difference of Two Normal Means	p. 339
Introduction	p. 339
Fixed-Width Confidence Intervals	p. 339
Minimum Risk Point Estimation	p. 355
Other Selected Multistage Procedures	p. 363
Some Selected Derivations	p. 366
Exercises	p. 369
Selecting the Best Normal Population	p. 375
Introduction	p. 375
Indifference-Zone Formulation	p. 377
Two-Stage Procedure	p. 380
Sequential Procedure	p. 382
Data Analyses and Conclusions	p. 384
Other Selected Multistage Procedures	p. 392
Some Selected Derivations	p. 395
Exercises	p. 402
Sequential Bayesian Estimation	p. 407
Introduction	p. 407
Selected Fixed-Sample-Size Concepts	p. 408
Elementary Sequential Concepts	p. 412
Data Analysis	p. 417
Exercises	p. 421
Selected Applications	p. 425
Introduction	p. 425
Clinical Trials	p. 426
Integrated Pest Management	p. 426
Experimental Psychology: Cognition of Distance	p. 429
A Problem in Horticulture	p. 432
Other Contemporary Areas of Applications	p. 438
Selected Reviews, Tables, and Other Items	p. 441
Introduction	p. 441
Big O(.) and Little o(.)	p. 441
Some Probabilistic Notions and Results	p. 442
A Glimpse at Nonlinear Renewal Theory	p. 446
Abbreviations and Notations	p. 449
Statistical Tables	p. 450
References	p. 455
Author Index	p. 479
Subject Index	p. 485
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Sequential Methods and Their Applications

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