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Singular asymptotic normality of an estimator in the conic section fitting problem. II


Author: S. V. Shklyar
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 93 (2015).
Journal: Theor. Probability and Math. Statist. 93 (2016), 177-196
MSC (2010): Primary 65D10; Secondary 62F12
DOI: https://doi.org/10.1090/tpms/1002
Published electronically: February 7, 2017
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Abstract: This is the second part of the author paper published in Theor. Probability and Math. Statist. 92 (2016), 147-161. The first part considers the functional version of the conic section fitting problem and states the asymptotic normality of the ALS2 estimator for the coefficients of the conic section. In the present paper, a similar theorem on the asymptotic normality is obtained for the structural model. Two estimators of the asymptotic covariance matrix are constructed. The consistency of both estimators is proved.


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Additional Information

S. V. Shklyar
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: shklyar@mail.univ.kiev.ua

DOI: https://doi.org/10.1090/tpms/1002
Keywords: Errors in variables, asymptotic normality, estimation of parameters of a conic section, estimation of the asymptotic variance
Received by editor(s): September 7, 2015
Published electronically: February 7, 2017
Additional Notes: This paper was prepared following the talk at the International conference “Probability, Reliability and Stochastic Optimization (PRESTO-2015)” held in Kyiv, Ukraine, April 7–10, 2015
Article copyright: © Copyright 2017 American Mathematical Society