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Optimal shrinkage estimator for high-dimensional mean vector
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0001-7855-8221
2019 (English)In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 170, p. 63-79Article in journal (Refereed) Published
Abstract [en]

In this paper we derive the optimal linear shrinkage estimator for the high-dimensional mean vector using random matrix theory. The results are obtained under the assumption that both the dimension $p$ and the sample size $n$ tend to infinity in such a way that $p∕n\to c\in(0,\infty)$. Under weak conditions imposed on the underlying data generating mechanism, we find the asymptotic equivalents to the optimal shrinkage intensities and estimate them consistently. The proposed nonparametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically, with probability 1, the quadratic loss when $c\in(0,1)$. When $c\in(1,\infty)$ we modify the estimator by using a feasible estimator for the precision covariance matrix. To this end, an exhaustive simulation study and an application to real data are provided where the proposed estimator is compared with known benchmarks from the literature. It turns out that the existing estimators of the mean vector, including the new proposal, converge to the sample mean vector when the true mean vector has an unbounded Euclidean norm.

Place, publisher, year, edition, pages
2019. Vol. 170, p. 63-79
Keywords [en]
Large-dimensional asymptotics, Mean vector estimation, Random matrix theory, Shrinkage estimator
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:su:diva-164879DOI: 10.1016/j.jmva.2018.07.004ISI: 000457205300006OAI: oai:DiVA.org:su-164879DiVA, id: diva2:1280599
Available from: 2019-01-20 Created: 2019-01-20 Last updated: 2019-03-04Bibliographically approved

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