Improved confidence sets for the coefficients of a linear model with spherically symmetric errors
The authors consider a linear model \(Y=A\theta +\sigma \cdot \epsilon\) where the pdf of \(\epsilon\) is assumed to be spherically symmetric around zero and with finite variance-covariance matrix. They obtain confidence sets for the location parameter \(\theta\) using the James-Stein estimator for \(\theta\) when the \(\dim(\theta)\geq 3\) and show that the James-Stein confidence dominates the classical confidence sets with the same radius not only when error distribution is \(N(0,\sigma^ 2I)\) but also for uniform distribution, double exponential and multivariate t distribution.
scientific article; zbMATH DE number 3969886