Geodesic
The James–Stein procedure for a conditionally Gaussian regression
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2011), pp. 6-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper considers the problem of estimating a $p$-dimensional ($p\ge2$) mean vector of a multivariate conditionally normal distribution under quadratic loss. The problem of this type arises when estimating the parameters in a continuous time regression model with a non-Gaussian Ornstein–Uhlenbeck process. We propose a modification of the James–Stein procedure of the form $\theta^*(Y)=(1-c/\|Y\|)Y$, where $Y$ is an observation and $c>0$ is a special constant. This estimate allows one to derive an explicit upper bound for the quadratic risk and has a significantly smaller risk than the usual maximum likelihood estimator for the dimensions $p\ge2$. This procedure is applied to the problem of parametric estimation in a continuous time conditionally Gaussian regression model and to that of estimating the mean vector of a multivariate normal distribution when the covariance matrix is unknown and depends on some nuisance parameters.
Keywords: conditionally Gaussian regression model, improved estimation, James–Stein procedure, non-Gaussian Ornstein–Uhlenbeck process. 
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     author = {E. A. Pchelintsev},
     title = {The {James{\textendash}Stein} procedure for a~conditionally {Gaussian} regression},
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}
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E. A. Pchelintsev. The James–Stein procedure for a conditionally Gaussian regression. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2011), pp. 6-17. http://geodesic.mathdoc.fr/item/VTGU_2011_4_a1/

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