Unified improvements in estimation of a normal covariance matrix in high and low dimensions

Hisayuki Tsukuma and Tatsuya Kubokawa

Journal of Multivariate Analysis, 2016, vol. 143, issue C, 233-248

Abstract: The problem of estimating a covariance matrix in multivariate linear regression models is addressed in a decision-theoretic framework. This paper derives unified dominance results under a Stein-like loss, irrespective of order of the dimension, the sample size and the rank of the regression coefficients matrix. Especially, using the Stein–Haff identity, we develop a key inequality which is useful for constructing a truncated and improved estimator based on the information contained in the sample means or the ordinary least squares estimator of the regression coefficients. Also, a quadratic loss-like function is used to suggest alternative improved estimators with respect to an invariant quadratic loss.

Keywords: High dimension; Inadmissibility; Invariant loss; Moore–Penrose inverse; Statistical decision theory (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:143:y:2016:i:c:p:233-248

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DOI: 10.1016/j.jmva.2015.09.016

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