Advances in Stochastic Simulation Methods,9780817641078

Advances in Stochastic Simulation Methods

by ; ;
ISBN13: 9780817641078
ISBN10: 0817641076
Format: Hardcover
Pub. Date: 2000-06-01
Publisher(s): Birkhauser
List Price: $160.48

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Summary

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.

Table of Contents

Preface xiii
Contributors xv
List of Tables
xxi
List of Figures
xxv
Part I: Simulation Models
Solving the Nonlinear Algebraic Equations with Monte Carlo Method
3(14)
S. Ermakov
I. Kaloshin
Introduction
4(1)
Neumann-Ulam Scheme
4(3)
Simples Nonlinear Problems
7(10)
References
14(3)
Monte Carlo Algorithms For Neumann Boundary Value Problem Using Fredholm Representation
17(12)
Y. N. Kashtanov
I. N. Kuchkova
Introduction
17(1)
Integral Representation
18(1)
Monte Carlo Estimators
19(4)
The Two-Dimensional Case
23(3)
An Application to Navier-Stokes Equations
26(3)
References
28(1)
Estimation Errors for Functionals on Measure Spaces
29(88)
N. Golyandina
V. Nekrutkin
Introduction
29(4)
Strong Weakly-Continuous Derivatives
33(1)
General Results
34(61)
Differential Equation
95(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
40(7)
General stratification scheme
40(1)
Examples
41(4)
References
45(2)
The Multilevel Method of Dependent Tests
47(16)
Stefan Heinrich
Introduction
47(1)
The Standard Method of Dependent Tests
48(2)
The Multilevel Approach
50(2)
Integrals Depending on a Parameter
52(11)
References
60(3)
Algebraic Modelling and Performance Evaluation of Acyclic Fork-Join Queueing Networks
63(22)
Nikolai K. Krivulin
Introduction
63(2)
Preliminary Algebraic Definitions and Results
65(2)
Further Algebraic Results
67(1)
An Algebraic Model of Queueing Networks
68(4)
Fork-Join queueing networks
69(2)
Examples of network models
71(1)
A Monotonicity Property
72(2)
Bounds on the Service Cycle Completion Time
74(1)
Stochastic Extension of the Network Model
75(3)
Some properties of expectation
76(1)
Existence of the cycle time
77(1)
Calculating bounds on the cycle time
78(1)
Discussion and Examples
78(7)
References
81(4)
Part II: Experimental Designs
Analytical Theory of E-Optimal Designs for Polynomial Regression
85(68)
V. B. Melas
Introduction
85(1)
Statement of the Problem
86(1)
Duality Theorem
86(1)
The Number of Design Points
87(3)
Tchebysheff Designs
90(1)
Boundary Equation
91(2)
An Extremal Property of Positive Polynomial Representations
93(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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