Circular and linear regression : fitting circles and lines by least squares /: fitting circles and lines by least squares. (©2011)

• Record Type: Book
• Further Information: Note: Nikolai Chernov.
• Other Names: Chernov, Nikolai, 1956-2014
• Contents: Introduction and Historic Overview ; Classical regression; Errors-in-variables (EIV) model; Geometric fit; Solving a general EIV problem; Nonlinear nature of the "linear" EIV; Statistical properties of the orthogonal fit; Relation to total least squares (TLS); Nonlinear models: general overview; Nonlinear models: EIV versus orthogonal fit Fitting Lines ; Parametrization; Existence and uniqueness; Matrix solution; Error analysis: exact results; Asymptotic models: large n versus small σ; Asymptotic properties of estimators; Approximative analysis; Finite-size efficiency; Asymptotic efficiency Fitting Circles: Theory ; Introduction; Parametrization; (Non)existence; Multivariate interpretation of circle fit; (Non)uniqueness; Local minima; Plateaus and valleys; Proof of two valley theorem; Singular case Geometric Circle Fits ; Classical minimization schemes; Gauss–Newton method; Levenberg–Marquardt correction; Trust region; Levenberg–Marquardt for circles: full version; Levenberg–Marquardt for circles: reduced version; A modification of Levenberg–Marquardt circle fit; Späth algorithm for circles; Landau algorithm for circles; Divergence and how to avoid it; Invariance under translations and rotations; The case of known angular differences Algebraic Circle Fits ; Simple algebraic fit (Kåsa method); Advantages of the Kåsa method; Drawbacks of the Kåsa method; Chernov–Ososkov modification; Pratt circle fit; Implementation of the Pratt fit; Advantages of the Pratt algorithm; Experimental test; Taubin circle fit; Implementation of the Taubin fit; General algebraic circle fits; A real data example; Initialization of iterative schemes Statistical Analysis of Curve Fits; Statistical models; Comparative analysis of statistical models; Maximum likelihood estimators (MLEs); Distribution and moments of the MLE; General algebraic fits; Error analysis: a general scheme; Small noise and "moderate sample size"; Variance and essential bias of the MLE; Kanatani–Cramer–Rao lower bound; Bias and inconsistency in the large sample limit; Consistent fit and adjusted least squares Statistical Analysis of Circle Fits ; Error analysis of geometric circle fit; Cramer–Rao lower bound for the circle fit; Error analysis of algebraic circle fits; Variance and bias of algebraic circle fits; Comparison of algebraic circle fits; Algebraic circle fits in natural parameters; Inconsistency of circular fits; Bias reduction and consistent fits via Huber; Asymptotically unbiased and consistent circle fits ; Kukush–Markovsky–van Huffel method; Renormalization method of Kanatani: 1st order; Renormalization method of Kanatani: 2nd order Various "Exotic" Circle Fits; Riemann sphere; Simple Riemann fits; Riemann fit: the SWFL version; Properties of the Riemann fit; Inversion-based fits; The RTKD inversion-based fit; The iterative RTKD fit; Karimäki fit; Analysis of Karimäki fit; Numerical tests and conclusions Bibliography Index
• Publisher Details: Boca Raton : Taylor & Francis
• Publication Date: 2011
• Copyright Date: 2011
• Extent: 1 online resource (xxx. 256 pages), illustrations
• Subjects: 519.5/35; Regression analysis; Curve fitting; Least squares; MATHEMATICS -- Applied; MATHEMATICS -- Probability & Statistics -- General; Curve fitting; Least squares; Regression analysis; Electronic books
• Languages: English
• ISBNs: 9781439835913; 1439835918
• Related ISBNs: 9781439835906; 143983590X
• Notes: Note: Includes bibliographical references (pages 241-253) and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.