Minimax estimators in linear models with restricted parameter space
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.
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