Fitting geometric curves to observed data
نویسنده
چکیده
Contents Preface v Chapter 1. Introduction and historic overview 1 1.1. Classical regression 1 1.2. Errors-in-variables (EIV) model 3 1.3. Geometric fit 5 1.4. Solving a general EIV problem 8 1.5. Non-linear nature of the 'linear' EIV 11 1.6. Statistical properties of the orthogonal fit 13 1.7. Relation to total least squares (TLS) 15 1.8. Nonlinear models 16 1.9. Notation and preliminaries 17 Chapter 2. Fitting lines 19 2.1. Parametrization 19 2.2. Existence and uniqueness 21 2.3. Matrix solution 23 2.4. Error analysis: exact results 25 2.5. Asymptotic models: large n versus small σ 27 2.6. Asymptotic properties of estimators 28 2.7. Approximative analysis 32 2.8. Finite-size efficiency 33 2.9. Asymptotic efficiency 35 Chapter 3. Fitting circles: theory 37 3.
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