  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.
