Statistics – Methodology
Scientific paper
2012-03-22
Statistical Science 2012, Vol. 27, No. 1, 61-81
Statistics
Methodology
Published in at http://dx.doi.org/10.1214/11-STS380 the Statistical Science (http://www.imstat.org/sts/) by the Institute of M
Scientific paper
10.1214/11-STS380
Let $X$ be a random vector with distribution $P_{\theta}$ where $\theta$ is an unknown parameter. When estimating $\theta$ by some estimator $\varphi(X)$ under a loss function $L(\theta,\varphi)$, classical decision theory advocates that such a decision rule should be used if it has suitable properties with respect to the frequentist risk $R(\theta,\varphi)$. However, after having observed $X=x$, instances arise in practice in which $\varphi$ is to be accompanied by an assessment of its loss, $L(\theta,\varphi(x))$, which is unobservable since $\theta$ is unknown. A common approach to this assessment is to consider estimation of $L(\theta,\varphi(x))$ by an estimator $\delta$, called a loss estimator. We present an expository development of loss estimation with substantial emphasis on the setting where the distributional context is normal and its extension to the case where the underlying distribution is spherically symmetric. Our overview covers improved loss estimators for least squares but primarily focuses on shrinkage estimators. Bayes estimation is also considered and comparisons are made with unbiased estimation.
Fourdrinier Dominique
Wells Martin T.
No associations
LandOfFree
On Improved Loss Estimation for Shrinkage Estimators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Improved Loss Estimation for Shrinkage Estimators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Improved Loss Estimation for Shrinkage Estimators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-381842