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Theory of Probability and Mathematical Statistics



On minimax estimators of regression models parameters

A. V. Ivanov, I. K. Matsak

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Abstract: For linear regression model and in certain sense uniform regression experiment design, an enhanced weak consistency property of vector regression parameter minimax estimator and limit theorem for extreme absolute values of residuals consructed by this estimator are obtained.

Keywords: Lenear regression model, extreme values, triangular array, minimax estimators, symmetric observation errors.

Bibliography:
1. A. V. Ivanov, I. K. Matsak, S. V. Polotskiy, Extreme residuals in regression model. Minimax approach , Modern stochastics : theory and applications, 2 (2015), no. 3, p. 297-308.
2. W. Feller, An introduction to probability theory and its applications . vol.2, Wiley, New York ‒ London ‒ Sydney, 1971.
3. B. V. Gnedenko, Sur la distribution limit du terme maximum d`une serie aleatoire , Ann.Math., 44 (1943), p. 423-453.
4. J. Galambos, The asymptotic theory of extreme order statistics , Wiley, New York, 1978.
5. M. R. Leadbetter, G. Lindgren, H. Rootzen, Extremes and related properties of random sequences and processes , Springer, New York ‒ Berlin, 1983.
6. V. M. Zolotarev, Modern Theory of Summation of Random Variable , VSP, Utreht, 1997.
7. J. Pfanzagl, On the Measurability and Consistency of Minimum Contrast Estimates , Metrika, (1969), No 14 , p. 249-272.
8. O. V. Ivanov, I. K. Matsak, Limit theorems for extreme residuals in linear and nonlinear regression models , Theor. Probability and Math. Statist., 86 (2013), 79-91.
9. O. V. Ivanov, I. K. Matsak, Limit theorems for extreme residuals in regression models with heavy tails of observation errors , Theor. Probability and Math. Statist., 88 (2014), 85-98.