A new estimator of covariance matrix

Further results on estimation of covariance matrix

“…It is worth mentioning that Ma et al (2012) treated the case m > p + 1 when β = 0 and Kubokawa et al (1992) considered the case α = 0 under the loss (2.2) with a known nonnegative-definite weighted matrix. Note that when α = 0,  Θ MEM is reduced to…”

“…Here it is interesting to note that when q 1 = · · · = q m = 1, the condition in Theorem 2.1 can be used to obtain the relevant result in Tsukuma and Kubokawa (2007) for the case of m > p + 1. On the other hand, applying Theorem 2.1 for β = 0, the relevant result in Ma et al (2012) can be obtained readily.…”

“…(2.9) Different from Ma et al (2012), we will use the unique unbiased estimator to obtain the sufficient conditions for the modified Efron-Morris estimator to be minimax under the loss (2.2). And the following several lemmas are needed.…”

“…Since James and Stein (1961), many papers have reported on improved estimators of the population covariance matrix from a decision-theoretic perspective (Efron and Morris, 1976) or from a Bayesian point of view (Daniels and Kass, 1999;Yang and Berger, 1994). Based on the work of Kubokawa et al (1992) and Ma et al (2012), the problem of estimating the covariance matrix Σ of a multivariate normal population is reconsidered in this paper from a decision-theoretic perspective. As we all know, the usual estimator of Σ is S/k, where S is distributed according to the Wishart distribution W p (Σ, k).…”

“…Specifically, we will use the so-called partial Iwasawa coordinates of covariance matrix to obtain a new estimator that dominates  Σ JS . Of course, our approach also builds on the work of Kubokawa et al (1992) and Ma et al (2012). The paper is structured as follows.…”