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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 45, Fasc. 2,
pages 211 - 225
DOI: 10.37190/0208-4147.00256
Published online 1.2.2026
 

Minimax estimators in linear models with restricted parameter space

M. Kowal
M. Wilczyński

Abstract:

In the paper we consider estimation of the regression coefficients in a linear regression model Y=Xβ+ε where β is assumed to lie in a given ellipsoid Θ The estimation is performed using a weighted squared error loss function. Under specific conditions, we find an explicit formula for an estimator β_M of β which is minimax in the class D of all decision rules, not limited to linear estimators. We generalize the results of Wilczyński (2007), who found a minimax decision rule β_M under considerably more restrictive conditions.

2010 AMS Mathematics Subject Classification: Primary 62H12; Secondary 62C20, 62J05, 62F30.

Keywords and phrases:

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