Advances in Stochastic Simulation Methods

, by Balakrishnan, N.; Melas, Viatcheslav B.; Ermakov, Sergei M.

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ISBN: 9780817641078 | 0817641076
Cover: Hardcover
Copyright: 6/1/2000

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Provides a survey of results and trends in the important areas of statistical modeling, experimental design, and related issues of mathematical statistics and computational mathematics. Shows the connection between different trends of fundamental research. DLC: Mathematical statistics--Data processing.

Preface

xiii

Contributors

List of Tables

xxi

List of Figures

xxv

Part I: Simulation Models

Solving the Nonlinear Algebraic Equations with Monte Carlo Method

(14)

S. Ermakov

I. Kaloshin

Introduction

(1)

Neumann-Ulam Scheme

(3)

Simples Nonlinear Problems

(10)

References

(3)

Monte Carlo Algorithms For Neumann Boundary Value Problem Using Fredholm Representation

(12)

Y. N. Kashtanov

I. N. Kuchkova

Introduction

(1)

Integral Representation

(1)

Monte Carlo Estimators

(4)

The Two-Dimensional Case

(3)

An Application to Navier-Stokes Equations

(3)

References

(1)

Estimation Errors for Functionals on Measure Spaces

(88)

N. Golyandina

V. Nekrutkin

Introduction

(4)

Strong Weakly-Continuous Derivatives

(1)

General Results

(61)

Differential Equation

(8)

Limiting Design

103

(6)

Taylor Expansion

109

(1)

Particular Cases

110

(7)

Boundary equation

110

(1)

Matrices J1(0) and vectors Jz2(0)

111

(1)

Tables of coefficients

112

(1)

Studying of convergence radius

113

(1)

References

114

(3)

Bias Constrained Minimax Robust Designs for Misspecified Regression Models

117

(18)

Douglas P. Wiens

Introduction

117

(1)

General Theory

118

(4)

Fitting a Second Order Response in Several Regressors

122

(1)

S an ellipsoid

122

(1)

S a q-dimensional rectangle

123

(1)

Fitting a Polynomial Response

123

(2)

Wavelet Regression

125

(1)

Extrapolation Designs

126

(2)

Extrapolation of a polynomial fit

127

(1)

Extrapolation of a first order response in several variables

128

(1)

Lack of Fit Testing

128

(2)

Generalized M-Estimation

130

(5)

References

130

(5)

A Comparative Study of MV- and SMV-Optimal Designs for Binary Response Models

135

J. Lopez-Fidalgo

W. K. Wong

Introduction

135

(4)

MV- and SMV-Optimal Designs

139

(5)

Logistic model

139

(4)

Double exponential model

143

(1)

Robustness Properties of MV- and SMV-Optimal Designs

144

(2)

Conclusions

146

References

150

Stratification

(7)

General stratification scheme

(1)

Examples

(4)

References

(2)

The Multilevel Method of Dependent Tests

(16)

Stefan Heinrich

Introduction

(1)

The Standard Method of Dependent Tests

(2)

The Multilevel Approach

(2)

Integrals Depending on a Parameter

(11)

References

(3)

Algebraic Modelling and Performance Evaluation of Acyclic Fork-Join Queueing Networks

(22)

Nikolai K. Krivulin

Introduction

(2)

Preliminary Algebraic Definitions and Results

(2)

Further Algebraic Results

(1)

An Algebraic Model of Queueing Networks

(4)

Fork-Join queueing networks

(2)

Examples of network models

(1)

A Monotonicity Property

(2)

Bounds on the Service Cycle Completion Time

(1)

Stochastic Extension of the Network Model

(3)

Some properties of expectation

(1)

Existence of the cycle time

(1)

Calculating bounds on the cycle time

(1)

Discussion and Examples

(7)

References

(4)

Part II: Experimental Designs

Analytical Theory of E-Optimal Designs for Polynomial Regression

(68)

V. B. Melas

Introduction

(1)

Statement of the Problem

(1)

Duality Theorem

(1)

The Number of Design Points

(3)

Tchebysheff Designs

(1)

Boundary Equation

(2)

An Extremal Property of Positive Polynomial Representations

(60)

On the Criteria for Experimental Design in Nonlinear Error-In-Variables Models

153

(12)

Silvelyn Zwansig

Introduction

153

(3)

Error-In-Variables Model

156

(1)

The Total Least Squares Estimator

157

(3)

Asymptotic normality and the Hajek bound

159

(1)

The Alternative Estimator

160

(2)

Conclusions

162

(3)

References

163

(2)

On Generating and Classifying all qn-m-1 Regularly Blocked Factional Designs

165

(12)

P. J. Laycock

P. J. Rowley

Introduction

165

(3)

The Algorithm

168

(2)

Some Specimens

170

(7)

n = 10, k = 7, l = 2, q = 2

170

(1)

n = 8, k = 6, l = 3, q = 2

171

(1)

n = 7, k = 4, various l, q = 3

172

(2)

Some q = 4 examples

174

(1)

References

175

(2)

Locally Optimal Designs in Non-Linear Regression: A Case Study of the Michaelis-Menten Function

177

(12)

E. P. J. Boer

D. A. M. K. Rasch

E. M. T. Hendrix

Introduction

177

(1)

Calculation of Optimal Design

178

(2)

Replicationfree designs

178

(1)

Unrestricted designs

178

(2)

Results

180

(5)

Optimal replicationfree designs

181

(1)

Optimal unrestricted designs

182

(3)

Non-convexity of the continuous NLP formulation

185

(1)

Conclusions

185

(4)

References

187

(2)

D-Optimal Designs for Quadratic Regression Models

189

(8)

E. E. M. van Berkum

B. Pauwels

P. M. Upperman

Introduction

189

(1)

D-Optimal Designs

190

(1)

Optimality of the Designs

191

(3)

Conclusion

194

(3)

References

194

(3)

On the Use of Symmetry in Optimal Design of Experiments

197

(10)

Vladimir Soloviov

Symmetry in Convex Optimization Problems

197

(1)

Optimal Design of Experiments

198

(2)

Optimal Designs for Polynomial Regression

200

(7)

References

203

(4)

Part III: Statistical Inference

Higher Order Moments of Order Statistics from the Pareto Distribution and Edgeworth Approximate Inference

207

(38)

Aaron Childs

K. S. Sultan

N. Balakrishnan

Introduction

207

(2)

Blue's of &thetas; and σ

209

(3)

Exact Expressions for the Moments of Order Statistics

212

(3)

Single moments of order statistics

213

(1)

Double moments of order statistics

213

(1)

Triple moments of order statistics

214

(1)

Quadruple moments of order statistics

215

(1)

Recurrence Relations for Moments of Order Statistics

215

(6)

Relations for single moments

215

(1)

Relations for double moments

216

(1)

Relations for triple moments

217

(1)

Relations for quadruple moments

218

(3)

Approximate Inference

221

(1)

Numerical Illustration

222

(2)

Recurrence Relations for Moments of Order Statistics in the Doubly Truncated Case

224

(21)

Relations for single moments

225

(1)

Relations for double moments

225

(1)

Relations for triple moments

226

(2)

Relations for quadruple moments

228

(3)

References

231

(14)

Higher Order Moments of Order Statistics from the Power Function Distribution and Edgeworth Approximate Inference

245

(38)

K. S. Sultan

Aaron Childs

N. Balakrishnan

Introduction

245

(2)

Blue's of &thetas; and σ

247

(3)

Exact Expressions for the Moments of Order Statistics

250

(3)

Single moments of order statistics

251

(1)

Double moments of order statistics

251

(1)

Triple moments of order statistics

252

(1)

Quadruple moments of order statistics

253

(1)

Recurrence Relations for Moments of Order Statistics

253

(6)

Relations for single moments

253

(1)

Relations for double moments

254

(1)

Relations for triple moments

255

(2)

Relations for quadruple moments

257

(2)

Approximate Inference

259

(2)

Numerical Illustration

261

(2)

Recurrence Relations for Moments of Order Statistics in the Doubly Truncated Case

263

(20)

Relations for single moments

263

(1)

Relations for double moments

264

(1)

Relations for triple moments

265

(2)

Relations for quadruple moments

267

(3)

References

270

(13)

Selecting from Normal Populations the One with the Largest Absolute Mean: Comon Unknown Variance Case

283

(10)

S. Jeyaratnam

S. Panchapakesan

Introduction

283

(2)

Proposed Procedure Rt

285

(3)

Approximation for h

288

(1)

Expected Sample Size

288

(1)

Concluding Remarks

289

(4)

References

292

(1)

Conditional Inference for the Parameters of Pareto Distributions when Observed Samples are Progressively Censored

293

(12)

Rita Aggarwala

Aaron Childs

Introduction

293

(3)

Best Linear Unbiased Estimation

296

(1)

Conditional Confidence Intervals

297

(2)

Conditional Tolerance Intervals

299

(1)

An Example

300

(1)

Sensitivity Analysis

300

(5)

References

301

(4)

Part IV: Applied Statistics and Related Topics

On Randomizing Estimators in Linear Regression Models

305

(10)

S. Ermakov

R. Schwabe

Some Properties of the Δ2 Distribution

306

(1)

Least Squares Estimators and Their Randomization

307

(4)

Δ2-Distribution in Experimental Design

311

(4)

References

313

(2)

Nonstationary Generalized Automata with Periodically Variable Parameters and Their Optimization

315

(22)

A. Yu. Ponomareva

M. K. Tchirkov

Introduction

315

(1)

Base Definitions and Problem Setting

316

(1)

The Basic Matrices of the Automaton Agv

317

(2)

Algorithms for Construction of the Families of Basic Matrices

319

(1)

Two Properties of Basic Matrices

320

(1)

Reduces and Minimal Forms of the Automaton

321

(1)

Theorems on Reduced Forms

322

(7)

Theorems on Minimal Forms

329

(2)

The Algorithm of Optimization

331

(1)

Example

331

(6)

References

335

(2)

Power of Some Asymptotic Tests for Maximum Entropy

337

(18)

M. Salicru

S. Vives

J. Ocana

Introduction

337

(2)

Taylor Series Approximations

339

(2)

A Simulation Study

341

(2)

Results and Discussion

343

(2)

Expectation and Variance of the Havrda-Charvat Entropies

345

(3)

Expectation and Variance of the Functional = (h,&phis;)-Entropies

348

(2)

Tables

350

(5)

Tables of simulation results

350

(1)

References

351

(4)

Partially Inversion of Functions for Statistical Modelling of Regulatory Systems

355

(18)

A. G. Bart

N. P. Alexeyeff (Klochkova)

N. Botchkina

Introduction

355

(1)

A Method for Partial Inversion of Functions

356

(3)

The parametrical description of the partial inverse functions

356

(2)

Double inversion

358

(1)

Generalised Binomial Distributions

359

(3)

Applications of Fiducial Distributions to Neurophysiology

362

(1)

Advertisement for Sales Marketing

363

(10)

Sanogenesis (compensation) curve

363

(4)

Example

367

(1)

Appendix

368

(2)

References

370

(3)

Simple Efficient Estimation for Three-Parameter Lognormal Distributions with Applications to Emissions Data and State Traffic Rate Data

373

(12)

N. Balakrishnan

Jun Wang

Introduction

373

(1)

Explicit Estimators

374

(1)

Simulation Results

375

(2)

Illustrative Examples

377

(3)

Conclusing Remarks

380

(5)

References

380

(5)

Subject Index

385

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Advances in Stochastic Simulation Methods

Summary

Table of Contents

Supplemental Materials