Pseudosolution of Linear Functional Equations: Parameters Estimation of Linear Functional Relationships (Mathematics and Its Applications)

✍ Scribed by Alexander S. Mechenov

• Year: 2005
• Tongue: English
• Leaves: 249
• Edition: 1
• Category: Library

✦ Synopsis

This book presents the author’s new method of two-stage maximization of a likelihood function, which helps to solve a series of non-solving before the well-posed and ill-posed problems of pseudosolution computing systems of linear algebraic equations (or, in statistical terminology, parameters’ estimators of functional relationships) and linear integral equations in the presence of deterministic and random errors in the initial data. This book presents, for the first time, a solution of the problem of reciprocal influence of passive errors of regressors and of active errors of predictors by computing point estimators of functional relationships.

✦ Table of Contents

Cover......Page 1
Mathematics and Its Applications......Page 3
PSEUDOSOLUTION OF LINEAR FUNCTIONAL EQUATIONS: Parameters Estimation of Linear Functional Relationships......Page 4
Copyright - ISBN: 0387245057......Page 5
Contents......Page 6
General Preface......Page 8
Labels and Abbreviations......Page 10
1. ANALYSIS OF PASSIVE EXPERIMENTS......Page 12
1.1 Multiple Linear Regression Analysis......Page 13
1.2 Linear Model Subject to the Linear Constraints......Page 24
1.3 Estimation of the Normal Parameter Vector......Page 29
1.4 Confluent analysis of Passive Experiment......Page 47
1.5 Stable Parameter estimation of the Degenerated Confluent Model......Page 67
1.6 Confluent-Regression Analysis of Passive Experiment......Page 78
1.7 Stable Estimation of Normal Parameters of the Degenerated Confluent-Regression Model......Page 95
2. ANALYSIS OF ACTIVE AND COMPLICATED EXPERIMENTS......Page 104
2.1 Analysis of Active Experiment......Page 105
2.2 Analysis of Active-Regression Experiment......Page 122
2.3 Analysis of Passive-Active Experiment......Page 128
2.4 Analysis of Passive-Active-Regression Experiment......Page 138
3.1 Variational Problems for the Construction of Pseudosolutions of Linear Integral Equations......Page 152
3.2 About the Appurtenance of Gauss-Markov Processes to Probability Sobolev Spaces......Page 177
3.3 Fredholm Linear Integral Equations with the Random Right-Hand Side Errors......Page 193
3.4 Linear Integral Equation with the Measured or Realized Core......Page 198
3.5 Technique of Computations......Page 212
References......Page 224
Application......Page 232
G......Page 240
R......Page 241
W......Page 242
Glossary of symbols......Page 244