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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
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 99 (2018).
Journal: Theor. Probability and Math. Statist. 99 (2019), 91-99
MSC (2010): Primary 60G70, 62J05
DOI: https://doi.org/10.1090/tpms/1082
Published electronically: February 27, 2020
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

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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
Email: alexntuu@gmail.com

I. K. Matsak
Affiliation: Taras Shevchenko National University, Academician Glushkov Avenue, 2, Building 6, Kyiv, 03127 Ukraine
Email: mik@unicyb.kiev.ua

DOI: https://doi.org/10.1090/tpms/1082
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