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Theory of Probability and Mathematical Statistics

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Minimax estimators of parameters of a regression model

Authors: A. V. Ivanov and I. K. Matsak
Translated by: S. V. Kvasko
Journal: Theor. Probability and Math. Statist. 99 (2019), 91-99
MSC (2010): Primary 60G70, 62J05
Published electronically: February 27, 2020
MathSciNet review: 3908658
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Abstract: We prove a stronger version of the weak consistency of a minimax estimator of a vector regression parameter and prove a limit theorem for absolute values of extreme residuals constructed from this estimator in a linear regression model and for the uniform design of the regression experiment.

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Additional Information

A. V. Ivanov
Affiliation: Department of Mathematical Analysis and Probability Theory, Department of Physics and Mathematics, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Peremogy Avenue, 37, Kyiv, 03057 Ukraine

I. K. Matsak
Affiliation: Taras Shevchenko National University, Academician Glushkov Avenue, 2, Building 6, Kyiv, 03127 Ukraine

Keywords: Linear regression model, extreme values, scheme of series, minimax estimators, symmetric errors of observations
Received by editor(s): July 2, 2018
Published electronically: February 27, 2020
Article copyright: © Copyright 2020 American Mathematical Society