Afrika Statistika

Quadratic loss estimation of a location parameter when a subset of its components is unknown

Idir Ouassou and Mustapha Rachdi

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Abstract

We consider the problem of estimating the quadratic loss $||\delta -\theta ||^{2}$ of an estimator $\delta $ of the location parameter $\theta =(\theta _{1},\ldots ,\theta _{p})$ when a subset of the components of $\theta$ are restricted to be nonnegative. First, we assume that the random observation $X$ is a Gaussian vector and, secondly, we suppose that the random observation has the form $(X,U)$ and has a spherically symmetric distribution around a vector of the form $(\theta ,0)$ with $\dim X=\dim \theta =p$ and $\dim U=\dim 0=k$. For these two settings, we consider two location estimators, the least square estimator and a shrinkage estimators, and we compare theirs unbiased loss estimators with improved loss estimator.

Article information

Source
Afr. Stat., Volume 8, Number 1 (2013), 561-575.

Dates
First available in Project Euclid: 5 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.as/1388953758

Digital Object Identifier
doi:10.4314/afst.v8i1.5

Mathematical Reviews number (MathSciNet)
MR3161753

Zentralblatt MATH identifier
1281.62043

Subjects
Primary: 62C20: Minimax procedures 62C15: Admissibility
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures

Keywords
Spherical symmetry Quadratic loss Least square estimator Unbiased loss estimator James-Stein estimation Minimaxity

Citation

Ouassou, Idir; Rachdi, Mustapha. Quadratic loss estimation of a location parameter when a subset of its components is unknown. Afr. Stat. 8 (2013), no. 1, 561--575. doi:10.4314/afst.v8i1.5. https://projecteuclid.org/euclid.as/1388953758


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