Theory of Probability and Mathematical Statistics
Singular asymptotic normality of an estimator in the conic section fitting problem. I
S. V. Shklyar
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Abstract: The conic section fitting problem is considered. True points are assumed to lie on a conic section. The points are observed with additive errors, which are independent and have bivariate normal distribution N(0,σ^2I) with unknown σ^2. We study asymptotic properties of the estimator of conic section parameters introduced by Kukush, Markovsky, and Van Huffel in Computational Statistics and Data Analysis 47 (2004), 123-147. Sufficient conditions for singular asymptotic normality of the estimator are provided. The asymptotic covariance matrix is singular and has defect 1 because the unit sphere in Euclidean space is taken as a parameter space.
Keywords: Errors in variables, asymptotic normality, estimation of parameters of a conic section
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