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

Full-text PDF

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.

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O. V. Ivanov and I. K. Matsak,
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O. V. Ivanov and I. K. Matsak,
*Limit theorems for extreme residuals in regression models with heavy tails of observation errors*, Teor. Imovirnost. ta Matem. Statyst.**88**(2013), 85-98; English transl. in Theor. Probability and Math. Statist.**88**(2014), 99-108. MR**3112637**

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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