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Regression Analysis Under A Priori Parameter Restrictions

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  • © 2012

Overview

Authors:
  1. Pavel S. Knopov

    1. VM Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kiev, Ukraine

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  2. Arnold S. Korkhin

    1. , Department of Economical Cybernetics and, National Mining University, Dnepropetrovsk, Ukraine

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  • Presents four central topics in stochastic optimization: calculation of parameter estimates, the asymptotic theory of estimates, estimation theory for small samples, and prediction theory
  • Describes applications to practical problems from various areas of study including econometrics, clinical medicine, and several other experimental sciences
  • Considers the problems of prediction by means of linear regression in the context of small samples

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 54)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Estimation of Regression Model Parameters with Specific Constraints

    • Pavel S. Knopov, Arnold S. Korkhin
    Pages 1-28

  3. Asymptotic Properties of Parameters in Nonlinear Regression Models

    • Pavel S. Knopov, Arnold S. Korkhin
    Pages 29-71

  4. Method of Empirical Means in Nonlinear Regression and Stochastic Optimization Models

    • Pavel S. Knopov, Arnold S. Korkhin
    Pages 73-120

  5. Determination of Accuracy of Estimation of Regression Parameters Under Inequality Constraints

    • Pavel S. Knopov, Arnold S. Korkhin
    Pages 121-181

  6. Asymptotic Properties of Recurrent Estimates of Parameters of Nonlinear Regression with Constraints

    • Pavel S. Knopov, Arnold S. Korkhin
    Pages 183-210

  7. Prediction of Linear Regression Evaluated Subject to Inequality Constraints on Parameters

    • Pavel S. Knopov, Arnold S. Korkhin
    Pages 211-221

  8. Back Matter

    Pages 223-234
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Keywords

About this book

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

Authors and Affiliations

  • VM Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    Pavel S. Knopov

  • , Department of Economical Cybernetics and, National Mining University, Dnepropetrovsk, Ukraine

    Arnold S. Korkhin

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