Statistical efficiency of curve fitting algorithms

Details Statistical efficiency of curve fitting algorithms Statistical efficiency of curve fitting algorithms

2003-03-18

arxiv.org/abs/cs/0303015v1

Computer Science

Computer Vision and Pattern Recognition

17 pages, 3 figures

Scientific paper

We study the problem of fitting parametrized curves to noisy data. Under certain assumptions (known as Cartesian and radial functional models), we derive asymptotic expressions for the bias and the covariance matrix of the parameter estimates. We also extend Kanatani's version of the Cramer-Rao lower bound, which he proved for unbiased estimates only, to more general estimates that include many popular algorithms (most notably, the orthogonal least squares and algebraic fits). We then show that the gradient-weighted algebraic fit is statistically efficient and describe all other statistically efficient algebraic fits.

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