Ebook: Regression Analysis Under A Priori Parameter Restrictions

This monograph focuses on the construction of regression models with linear and non-linear constrain inequalities from the theoretical point of view. Unlike previous publications, this volume analyses the properties of regression with inequality constrains, investigating the flexibility of inequality constrains and their ability to adapt in the presence of additional a priori information The implementation of inequality constrains improves the accuracy of models, and decreases the likelihood of errors. Based on the obtained theoretical results, a computational technique for estimation and prognostication problems is suggested. This approach lends itself to numerous applications in various practical problems, several of which are discussed in detail The book is useful resource for graduate students, PhD students, as well as for researchers who specialize in applied statistics and optimization. This book may also be useful to specialists in other branches of applied mathematics, technology, econometrics and finance

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Construction of various models of objects under uncertainty is one of the most important problems in modern decision making theory. Regression models are some of the most prevalent tools for modeling under uncertainty and are widely applied in different branches of science such as in industrial research, agriculture, medicine, and business and economics. Regression Analysis Under A Priori Parameter Restrictions will be of interest to a broad spectrum of readers in applied mathematics, mathematical statistics, identification theory, systems analysis, econometrics, finance, optimization, and other scientific disciplines. Requiring a background in algebra, probability theory, mathematical statistics, and mathematical programming, this work may also be a useful supplement for advanced graduate courses in estimation theory, regression analysis, mathematical statistics, econometrics, mathematical programming and optimal control, and stochastic optimization.

The material contained in this monograph successfully combines interesting theoretical results with methods and algorithms for solving practical problems. Itfocuses on the construction of regression models with linear and non-linear constraint inequalities and is the first book in which the theoretical results lying in the background of construction and studying regression models with inequality constraints on parameters are presented systematically and solidly.

Problems are described and studied in a clear, precise, and rigorous method and include: calculation of estimates for regression parameters, determination of their asymptotic properties and accuracy of estimation, point and interval prediction by the regression, parameters of which are estimated under inequality constraints. The authors’ approach lends itself to numerous applications in various practical problems, several of which are discussed in detail.

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Construction of various models of objects under uncertainty is one of the most important problems in modern decision making theory. Regression models are some of the most prevalent tools for modeling under uncertainty and are widely applied in different branches of science such as in industrial research, agriculture, medicine, and business and economics. Regression Analysis Under A Priori Parameter Restrictions will be of interest to a broad spectrum of readers in applied mathematics, mathematical statistics, identification theory, systems analysis, econometrics, finance, optimization, and other scientific disciplines. Requiring a background in algebra, probability theory, mathematical statistics, and mathematical programming, this work may also be a useful supplement for advanced graduate courses in estimation theory, regression analysis, mathematical statistics, econometrics, mathematical programming and optimal control, and stochastic optimization.

The material contained in this monograph successfully combines interesting theoretical results with methods and algorithms for solving practical problems. Itfocuses on the construction of regression models with linear and non-linear constraint inequalities and is the first book in which the theoretical results lying in the background of construction and studying regression models with inequality constraints on parameters are presented systematically and solidly.

Problems are described and studied in a clear, precise, and rigorous method and include: calculation of estimates for regression parameters, determination of their asymptotic properties and accuracy of estimation, point and interval prediction by the regression, parameters of which are estimated under inequality constraints. The authors’ approach lends itself to numerous applications in various practical problems, several of which are discussed in detail.
Content:
Front Matter....Pages i-xiii
Estimation of Regression Model Parameters with Specific Constraints....Pages 1-28
Asymptotic Properties of Parameters in Nonlinear Regression Models....Pages 29-71
Method of Empirical Means in Nonlinear Regression and Stochastic Optimization Models....Pages 73-120
Determination of Accuracy of Estimation of Regression Parameters Under Inequality Constraints....Pages 121-181
Asymptotic Properties of Recurrent Estimates of Parameters of Nonlinear Regression with Constraints....Pages 183-210
Prediction of Linear Regression Evaluated Subject to Inequality Constraints on Parameters....Pages 211-221
Back Matter....Pages 223-234

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Construction of various models of objects under uncertainty is one of the most important problems in modern decision making theory. Regression models are some of the most prevalent tools for modeling under uncertainty and are widely applied in different branches of science such as in industrial research, agriculture, medicine, and business and economics. Regression Analysis Under A Priori Parameter Restrictions will be of interest to a broad spectrum of readers in applied mathematics, mathematical statistics, identification theory, systems analysis, econometrics, finance, optimization, and other scientific disciplines. Requiring a background in algebra, probability theory, mathematical statistics, and mathematical programming, this work may also be a useful supplement for advanced graduate courses in estimation theory, regression analysis, mathematical statistics, econometrics, mathematical programming and optimal control, and stochastic optimization.

The material contained in this monograph successfully combines interesting theoretical results with methods and algorithms for solving practical problems. Itfocuses on the construction of regression models with linear and non-linear constraint inequalities and is the first book in which the theoretical results lying in the background of construction and studying regression models with inequality constraints on parameters are presented systematically and solidly.

Problems are described and studied in a clear, precise, and rigorous method and include: calculation of estimates for regression parameters, determination of their asymptotic properties and accuracy of estimation, point and interval prediction by the regression, parameters of which are estimated under inequality constraints. The authors’ approach lends itself to numerous applications in various practical problems, several of which are discussed in detail.
Content:
Front Matter....Pages i-xiii
Estimation of Regression Model Parameters with Specific Constraints....Pages 1-28
Asymptotic Properties of Parameters in Nonlinear Regression Models....Pages 29-71
Method of Empirical Means in Nonlinear Regression and Stochastic Optimization Models....Pages 73-120
Determination of Accuracy of Estimation of Regression Parameters Under Inequality Constraints....Pages 121-181
Asymptotic Properties of Recurrent Estimates of Parameters of Nonlinear Regression with Constraints....Pages 183-210
Prediction of Linear Regression Evaluated Subject to Inequality Constraints on Parameters....Pages 211-221
Back Matter....Pages 223-234
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