Nonlinear Statistical Models

1. Front Matter

   Pages i-ix

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2. Introduction

   • Andrej Pázman

   Pages 1-6

3. Linear regression models

   • Andrej Pázman

   Pages 7-33

4. Linear methods in nonlinear regression models

   • Andrej Pázman

   Pages 34-54

5. Univariate regression models

   • Andrej Pázman

   Pages 55-79

6. The structure of a multivariate nonlinear regression model and properties of L ₂ estimators

   • Andrej Pázman

   Pages 80-112

7. Nonlinear regression models: computation of estimators and curvatures

   • Andrej Pázman

   Pages 113-130

8. Local approximations of probability densities and moments of estimators

   • Andrej Pázman

   Pages 131-153

9. Global approximations of densities of L ₂ estimators

   • Andrej Pázman

   Pages 154-191

10. Statistical consequences of global approximations especially in flat models

    • Andrej Pázman

    Pages 192-214

11. Nonlinear exponential families

    • Andrej Pázman

    Pages 215-247

12. Back Matter

    Pages 248-259

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Nonlinear statistical modelling is an area of growing importance. This monograph presents mostly new results and methods concerning the nonlinear regression model.
Among the aspects which are considered are linear properties of nonlinear models, multivariate nonlinear regression, intrinsic and parameter effect curvature, algorithms for calculating the L₂-estimator and both local and global approximation. In addition to this a chapter has been added on the large topic of nonlinear exponential families.
The volume will be of interest to both experts in the field of nonlinear statistical modelling and to those working in the identification of models and optimization, as well as to statisticians in general.

• Estimator
• Moment
• Parameter
• linear regression
• probability

• Faculty of Mathematics and Physics, Comenius University, Bratislava, Slovak Republic

  Andrej Pázman

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