Advances on Methodological and Applied Aspects of Probability and Statistics

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ISBN: 9781560329800 | 1560329807
Cover: Hardcover
Copyright: 4/24/2003

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This is one of two volumes that sets forth invited papers presented at the International Indian Statistical Association Conference. This volume emphasizes advancements in methodology and applications of probability and statistics. The chapters, representing the ideas of vanguard researchers on the topic, present several different subspecialties, including applied probability, models and applications, estimation and testing, robust inference, regression and design and sample size methodology. The text also fully describes the applications of these new ideas to industry, ecology, biology, health, economics and management. Researchers and graduate students in mathematical analysis, as well as probability and statistics professionals in industry, will learn much from this volume.

Preface

xxi

List of Contributors

xxiii

List of Tables

xxix

List of Figures

xxxv

Part I Applied Probability

From Dams to Telecommunication - A Survey of Basic Models

(10)

N. U. Prabhu

Introduction

(1)

Moran's Model for the Finite Dam

(2)

A Continuous Time Model for the Dam

(2)

A Model for Data Communication Systems

(5)

References

(2)

Maximum Likelihood Estimation in Queueing Systems

(34)

U. Narayan Bhat

Ishwar V. Basawa

Introduction

(2)

M.L.E. in Markovian Systems

(1)

M.L.E. in Non-Markovian Systems

(2)

M.L.R. for Single Server Queues Using Waiting Time Data

(1)

M.L.E. Using System Time

(2)

M.L.E. in M/G/1 Using Queue Length Data

(3)

M.L.E. in GI/M/1 Using Queue Length Data

(2)

Some Observations

(6)

References

(5)

Numerical Evaluation of State Probabilities at Different Epochs in Multiserver GI/Geom/m Queue

M. L. Chaudhry

U. C. Gupta

Introduction

(1)

Model and Solution: GI/Geom/m (EAS)

(6)

Evaluation of {Qn}∞ from {Qn}∞

(2)

Outside observer's distribution

(1)

GI/Geom/m (LAS-DA)

(4)

Evaluation of {Pn}∞ from {Pn}∞

(1)

Outside observer's distribution

(1)

Numerical Results

(4)

References

(1)

Busy Period Analysis of GIbIM/1/N Queues - Lattice Path Approach

(40)

Kanwar Sen

Manju Agarwal

Introduction

(2)

The GIb/M/1/N Model

(1)

Lattice Path Approach

(1)

Discretized Cb2/M/1/N Model

(9)

Transient Probabilities

(1)

Counting of Lattice Paths

(1)

Notations

(7)

Busy Period Probability for the Discretized Cb2/M/1/N Model

(3)

Continuous Cb2/M/1/N Model

(1)

Particular Cases

(1)

Numerical Computations and Comments

(22)

References

(20)

Part II Models and Applications

Measures for Distributional Classification and Model Selection

(14)

Govind S. Mudholkar

Rajesehwari Natarajan

Introduction

(1)

Current Measures for Distributional Morphology

(3)

(ξ1,ξ2) System

(2)

Asymptotic Distributions of J1, J2

(2)

Miscellaneous Remarks

(6)

References

(4)

Modeling with a Bivariate Geometric Distribution

101

(12)

Sunil K. Dhar

Introduction

101

(1)

Interpretation of BVG Model Assumptions

102

(2)

The Model Under the Environmental Effect

104

(1)

Data Analysis with BVG Model

105

(8)

References

109

(4)

Part III Estimation and Testing

Small Area Estimation: Updates With Appraisal

113

(28)

J. N. K. RAO

Introduction

113

(2)

Small Area Models

115

(5)

Area Level Models

115

(3)

Unit Level Models

118

(2)

Model-Based Inference

120

(8)

EBLUP Method

121

(3)

EB Method

124

(1)

HE Method

125

(3)

Some Recent Applications

128

(13)

Area-level Models

128

(3)

Unit Level Models

131

(10)

References

Unimodality in Circular Data: A Bayes Test

141

(18)

Sanjib Basu

S. Rao Jammalamadaka

Introduction

141

(2)

Existing Literature

143

(1)

Mixture of Two Von-Mises Distributions

144

(2)

Prior Specification

146

(1)

Prior and Posterior Probability of Unimodality

147

(1)

The Bayes Factor

148

(1)

Application

149

(2)

Some Issues

151

(8)

References

153

(6)

Maximum Likelihood Estimation of the Laplace Parameters Based on Progressive Type-II Censored Samples

159

(10)

Rita Aggarwala

N. Balakrishnan

Introduction

159

(2)

Examining the Likelihood Function

161

(2)

Algorithm To Find Mle's

163

(2)

Numerical Example

165

(4)

References

166

(3)

Estimation of Parameters of the Laplace Distribution Using Ranked Set Sampling Procedures

169

(14)

Dinish S. Bhoj

Introduction

169

(2)

Estimation of Parameters Based on Three Procedures

171

(3)

Ranked Set Sampling

171

(1)

Modified Ranked Set Sampling

172

(1)

New Ranked Set Sampling

173

(1)

Laplace Distribution

174

(2)

Comparison of Estimators

176

(7)

Joint Estimation of μ and σ

176

(1)

Estimation of μ

177

(1)

Estimation of σ

177

(1)

References

178

(5)

Some Results on Order Statistics Arising in Multiple Testing

183

(14)

Sanat K. Sarkar

Introduction

183

(2)

The Monotonicity of di's

185

(2)

Results on Ordered Components of a Random Vector

187

(10)

References

191

(6)

Part IV Robust Inference

Robust Estimation Via Generalized L-Statistics: Theory, Applications, and Perspectives

197

(22)

Robert Serfling

Introduction

197

(3)

A Unifying Structure

198

(2)

Basic Formulation of GL-Statistics

200

(3)

Representation of GL-Statistics as Statistical Functionals

200

(2)

A More General Form of Functional

202

(1)

The Estimation Error

203

(1)

Some Foundational Tools

203

(5)

Differentation Methodology

203

(1)

The Estimation Error in the U-Empirical Process

204

(1)

Extended Glivenko-Cantelli Theory

205

(1)

Oscillation Theory, Generalized Order Statistics, and Bahadur Representations

206

(1)

Estimation of the Variance of a U-Statistic

207

(1)

General Results for U-Statistics

208

(2)

Asymptotic Normality and the LIL

208

(1)

The SLLN

209

(1)

Large Deviation Theory

209

(1)

Further Results

210

(1)

Some Applications

210

(9)

One-Sample Quantile Type Parameters

210

(2)

Two-Sample Location and Scale Problems

212

(1)

Robust ANOVA

213

(1)

Robust Regression

213

(1)

Robust Estimation of Exponential Scale Parameter

213

(1)

References

214

(5)

A Class of Robust Stepwise Tests For Manova

219

(22)

Deo Kumar Srivastava

Govind S. Mudholkar

Carol E. Marchetti

Introduction

220

(2)

Preliminaries

222

(5)

Robust Univariate Tests

222

(2)

Combining Independent P-Values

224

(1)

Modified Step Down Procedure

225

(2)

Robust Stepwise Tests

227

(1)

A Monte Carlo Experiment

228

(3)

The Study

228

(3)

Conclusions

231

(10)

References

231

(10)

Robust Estimators for the One-Way Variance Components Model

241

(22)

Yogendra P. Chaubey

K. Venkateswarlu

Introduction

241

(2)

Mixed Linear Models and Estimation of Parameters

243

(3)

General Mixed Linear Model

243

(1)

Maximum Likelihood and Restricted Maximum Likelihood Estimators

244

(1)

Robust Versions of ML and REML Estimators

245

(1)

Computation of Estimators for the One Way Model

246

(1)

Description of the Simulation Experiment

246

(2)

Discussion of the Results

248

(1)

Biases of the Estimators of σ2

248

(1)

Biases of the Estimators of σ2e

248

(1)

MSE's of Estimators of σ2a

248

(1)

MSE's of Estimators of σ2e

249

(1)

Summary and Conclusions

249

(14)

References

249

(14)

Part V Regression and Design

Performance of the PTE Based on the Conflicting W, LR and LM Tests in Regression Model

263

(20)

Md. Baki Billah

A. K. Md. E. Saleh

Introduction

264

(1)

The Tests and Proposed Estimators

265

(2)

BIAS, M and Risk of the Estimators

267

(2)

Relative Performance of the Estimators

269

(4)

Bias Analysis of the Estimators

269

(1)

M Analysis of the Estimators

270

(1)

Risk Analysis of the Estimators

271

(2)

Efficiency Analysis and Recommendations

273

(2)

Conclusion

275

(8)

References

276

(7)

Estimation of Regression and Dispersion Parameters in the Analysis of Proportions

283

(22)

Sudhir R. Paul

Introduction

284

(1)

Estimation

285

(4)

The Extended Beta-Binomial Likelihood

285

(1)

The Quasi-Likelihood Method

286

(1)

Estimation Using quadratic Estimating Equations

287

(2)

Asymptotic Relative Efficiency

289

(3)

Examples

292

(1)

Discussion

293

(12)

References

294

(11)

Semiparametric Location-Scale Regression Models For Survival Data

305

(20)

Xuewen Lu

R. S. Singh

Introduction

306

(1)

Likelihood Function for the Parametric Location-Scale Models

307

(1)

Generalized Profile Likelihood

308

(2)

Application of Generalized Profile Likelihood to Semiparametric Location-Scale Regression Models

308

(1)

Estimation and Large Sample Properties

309

(1)

Examples of Semiparametric Location-Scale Regression Models

310

(2)

An Example with Censored Survival Data: Primary Biliary Cirrhosis (PBC) Data

312

(13)

References

313

(1)

Appendix: Computation of the Estimates

314

(11)

Analysis of Saturated and Super-Saturated Factorial Designs: A Review

325

(24)

Kimberly K. J. Kinateder

Daniel T. Voss

Weizhen Wang

Introduction

325

(2)

Background

327

(4)

Orthogonality and Saturation

327

(2)

Control of Error Rates

329

(2)

Orthogonal Saturated Designs

331

(9)

Background

331

(2)

Simultaneous Stepwise Tests

333

(4)

Individual Tests

337

(1)

Individual Confidence Intervals

338

(1)

Simultaneous Confidence Intervals

338

(1)

Adaptive Methods

339

(1)

Non-Orthogonal Saturated Designs

340

(2)

Individual Confidence Intervals

341

(1)

Open Problems

342

(1)

Super-Saturated Designs

342

(7)

References

343

(6)

On Estimating Subject-Treatment Interaction

349

(18)

Gary Gadbury

Hari Iyer

Introduction

350

(2)

An Estimator of S2D Using Concomitant Information

352

(7)

An Illustrative Example

359

(1)

Summary/Conclusions

360

(7)

References

361

(6)

Part VI Sample Size Methodology

Advances in Sample Size Methodology for Binary Data Studies-A Review

367

(16)

M. M. Desu

Establishing Therapeutic Equivalence in Parallel Studies

367

(7)

Tests under Δ-Formulation (20.2)

369

(2)

Tests under Relative Risk Formulation (ψ Formulation)

371

(2)

Confidence Bound Method for Δ Formulation

373

(1)

Sample Size for Paired Data Studies

374

(9)

Testing for Equality of Correlated Proportions

375

(2)

Tests for Establishing Equivalence

377

(3)

References

380

(3)

Robustness of a Sample Size Re-Estimation Procedure in Clinical Trials

383

(18)

Z. Govindarajulu

Introduction

383

(2)

Formulation of the Problem

385

(1)

The Main Results

386

(9)

Fixed-Width Confidence Interval Estimation

395

(1)

References

396

(5)

Part VII Applications to Industry

Implementation of Statistical Methods in Industry

401

(12)

Bovas Abraham

Introduction

401

(1)

Levels of Statistical Need in Industry

402

(1)

Implementation General Issues

402

(2)

Implementation Via Training And/Or Consulting

404

(1)

Implementation Via Education

405

(1)

University-Industry Collaboration

406

(1)

University of Waterloo and Industry

406

(3)

Concluding Remarks

409

(4)

References

410

(3)

Sequential Designs Based on Credible Regions

413

(12)

Enrique Gonzalez

Josep Ginebra

Introduction

413

(2)

Designs for Control Based on H.P.D. Sets

415

(2)

An Example of the Use of HPD Designs

417

(1)

Designs For R.S.B. Based on C.P. Intervals

418

(2)

Concluding Remarks

420

(5)

Appendix: Model Used in Section 23.3

421

(1)

References

422

(3)

Aging with Laplace Order Conserving Survival Under Perfect Repairs

425

(16)

Manish C. Bhattacharjee

Sujit K. Basu

Introduction

425

(1)

The Class LD

426

(3)

Closure Properties

429

(5)

Coherent Structures

429

(2)

Convolutions

431

(2)

Mixtures

433

(1)

The Discrete Class GD and Its Dual

434

(2)

L and LD Aging with Shocks

436

(5)

References

440

(1)

Defect Rate Estimation Using Imperfect Zero-Defect Sampling with Rectification

441

(24)

Neerja Wadhwa

Introduction

441

(2)

Sampling Plan A

443

(9)

Model

443

(1)

Modification of Greenberg and Stokes Estimators

444

(2)

An Empirical Bayes Estimator

446

(2)

Comparison of Estimators

448

(2)

Example

450

(2)

Sampling Plan B

452

(2)

Estimators

452

(2)

Suggestions for Further Research

454

(11)

Appendix A1: Calculation of the Second Term in Unew,2

455

(1)

Appendix A2: Analytical Expressions for the Bias and MSE

456

(3)

References

459

(6)

Statistics in the Real World-What I've Learnt in My First Year (and a Half) in Industry

465

(12)

Rekha Agrawal

The GE Environment

465

(2)

Six Sigma

467

(1)

The Projects That I've Worked on

468

(3)

Introduction

468

(1)

New Product Launch

469

(1)

Reliability Issue with a Supplied Part

469

(1)

Constructing a Reliability Database

470

(1)

Some Surprises Coming to Industry

471

(3)

General Comments

474

(3)

References

474

(3)

Part VIII Applications to Ecology, Biology and Health

Contemporary Challenges and Recent Advances in Ecological and Environmental Sampling

477

(30)

G. P. Patil

C. Taillie

Certain Challenges and Advances in Transect Sampling

477

(9)

Deep-Sea Red Crab

478

(2)

Bivariate Sighting Functions

480

(2)

Guided Transect Sampling

482

(4)

Certain Challenges and Advances in Composite Sampling

486

(9)

Estimating Prevalence Using Composites

486

(5)

Two-Way Compositing

491

(1)

Compositing and Stochastic Monotonicity

492

(3)

Certain Challenges and Advances in Adaptive Cluster Sampling

495

(12)

Adaptive Sampling and GIS

495

(4)

Using Covariate-Species Community Dissimilarity to Guide Sampling

499

(4)

References

503

(4)

The Analysis of Multiple Neural Spike Trains

507

(18)

Satish Iyengar

Introduction

507

(1)

Physiological Background

508

(2)

Methods for Detecting Functional Connections

510

(11)

Moment Methods

510

(2)

Intensity Function Based Methods

512

(1)

Frequency Domain Methods

513

(3)

Graphical Methods

516

(2)

Parametric Methods

518

(3)

Discussion

521

(4)

References

521

(4)

Some Statistical Issues Involving Multigeneration Cytonuclear Data

525

(22)

Susmita Datta

Introduction

526

(1)

Neutrality or Selection?

527

(11)

Sampling Schemes for Multi-Generation Data

529

(1)

An Omnibus Test

530

(1)

Application to Gambusia Data

531

(1)

Application to Drosophila Melanogaster Data

532

(1)

Tests Against a Specific Selection Model

532

(6)

Inference for the Selection Coefficients

538

(9)

A Multiplicative Fertility Selection Model

539

(1)

An Approximate Likelihood

539

(2)

Application to Hypotheses Testing

541

(1)

References

541

(6)

The Performance of Estimation Procedures for Cost-Effectiveness Ratios

547

(14)

Joseph C. Gardiner

Alka Indurkhya

Zhehui Luo

Introduction

547

(1)

Confidence Intervals for Cer

548

(2)

Comparison of Intervals

550

(2)

Simulation Studies

552

(1)

Results

553

(5)

Recommendations

558

(3)

References

559

(2)

Modeling Time-To-Event Data Using Flowgraph Models

561

(14)

Aparna V. Huzurbazar

Introduction

561

(2)

Introduction to Flowgraph Modeling

563

(3)

Flowgraph Models for Series Systems

563

(1)

Flowgraph Models for Parallel Systems

564

(1)

Flowgraph Models with Feedback

565

(1)

Reliability Application: Hydraulic Pump System

566

(2)

Survival Analysis Application: A Feed Forward Model for HIV

568

(2)

Conclusion

570

(5)

References

571

(4)

Part IX Applications to Economics and Management

Information Matrix Tests for the Composed Error frontier Model

575

(22)

Anil K. Bera

Naresh C. Mallick

Introduction

575

(2)

Information Matrix Tests for Frontier Models

577

(7)

The Elements of the IM Test for the Output Model

577

(5)

The Elements of the IM Test for the Cost Model

582

(2)

Empirical Results

584

(5)

Output Model Estimation

584

(1)

Moments Test for the Output Model

585

(2)

Cost Model Estimation

587

(1)

Moments Test for the Cost Model

587

(2)

Conclusion

589

(8)

Appendix A

590

(2)

Appendix B

592

(3)

References

595

(2)

Generalized Estimating Equations for Panel Data and Managerial Monitoring in Electric Utilities

597

(1)

H. D. Vinod

R. R. Geddes

The Introduction and Motivation

597

(4)

Glm, Gee & Panel Logit/Probit (Ldv) Models

601

(4)

GLM for Panel Data

605

(1)

Random Effects Model from Econometrics

606

(1)

Derivation of GEE, the Estimator for β and Standard Errors

607

(2)

Gee Estimation of Ceo Turnover and Three Hypotheses

609

(2)

Description of Data

611

(2)

Shareholder and Consumer Wealth Variables for Hypothesis Testing

613

(1)

Empirical Results

614

(2)

Concluding Remarks

616

(1)

References

617

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Advances on Methodological and Applied Aspects of Probability and Statistics

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Table of Contents

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