A New Class of Improved Estimators of a Multinormal Precision Matrix

Dey, Dipak K.; Ghosh, Mrinalkanti; Srinivasan, Cidambi

doi:10.1524/strm.1990.8.2.141

Cited by 4 publications

(4 citation statements)

References 4 publications

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“…The dominance results under the loss function have been studied for n > p [3,5,9]. In the case of p > n, the risk function of δ(Φ) under the loss L 1 (δ, Σ ) is expressed as…”

Section: Dominance Results Relative To the L 1 -Lossmentioning

confidence: 99%

Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data

Kubokawa

Srivastava

2008

Journal of Multivariate Analysis

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In this article, the Stein-Haff identity is established for a singular Wishart distribution with a positive definite mean matrix but with the dimension larger than the degrees of freedom. This identity is then used to obtain estimators of the precision matrix improving on the estimator based on the Moore-Penrose inverse of the Wishart matrix under the Efron-Morris loss function and its variants. Ridge-type empirical Bayes estimators of the precision matrix are also given and their dominance properties over the usual one are shown using this identity. Finally, these precision estimators are used in a quadratic discriminant rule, and it is shown through simulation that discriminant methods based on the ridge-type empirical Bayes estimators provide higher correct classification rates.

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“…The dominance results under the loss function have been studied for n > p [3,5,9]. In the case of p > n, the risk function of δ(Φ) under the loss L 1 (δ, Σ ) is expressed as…”

Section: Dominance Results Relative To the L 1 -Lossmentioning

confidence: 99%

Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data

Kubokawa

Srivastava

2008

Journal of Multivariate Analysis

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“…In that case, Σ −1 , the inverse of the covariance matrix Σ, is often called the precision matrix. This classical multivariate setting has been studied by Efron and Morris [4], Haff [7], Dey [2], Krishnamoorthy and Gupta [13], Dey et al [3], Zhou et al [19], and Tsukuma and Konno [17]. Note that, in these papers, S is assumed to be invertible.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the inverse scatter matrix for a scale mixture of Wishart matrices under Efron–Morris type losses

Boukehil

Fourdrinier

Mezoued³

et al. 2021

Journal of Statistical Planning and Inference

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We consider estimation of the inverse scatter matrix Σ −1 for a scale mixture of Wishart matrices under various Efron-Morris type losses, tr[{Σ −1 − Σ −1 } 2 S k ] for k = 0, 1, 2..., where S is the sample covariance matrix. We improve on the standard estimators a S + , where S + denotes the Moore-Penrose inverse of S and a is a positive constant, through an unbiased estimator of the risk difference between the new estimators and a S + . Thus we demontrate that improvements over the standard estimators under a Wishart distribution can be extended under mixing. We give a unified treatement of the two cases where S is invertible (S + = S −1 ) and where S is singular.

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“…Of these, estimates of the inverse covariance matrix are required in many multivariate inference procedures including the Fisher linear discriminant analysis, confidence intervals based on the Mahalanobis distance, optimal portfolio selection, graphical models, and weighted least squares estimator in multivariate linear regression models. Estimation of the precision matrix in the classical multivariate setting has been studied by Efron and Morris [12], Haff [21], Dey [9], Krishnamoorthy and Gupta [24], Dey et al [10], Zhou et al [43], and Tsukuma and Konno [42].…”

Section: Introductionmentioning

confidence: 99%

Estimation of the inverse scatter matrix of an elliptically symmetric distribution

Fourdrinier

Mezoued

Wells

2016

Journal of Multivariate Analysis

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a b s t r a c tWe consider estimation of the inverse scatter matrices Σ −1 for high-dimensional elliptically symmetric distributions. In high-dimensional settings the sample covariance matrix S may be singular. Depending on the singularity of S, natural estimators of Σ −1 are of the form a S −1 or a S + where a is a positive constant and S −1 and S + are, respectively, the inverse and the Moore-Penrose inverse of S. We propose a unified estimation approach for these two cases and provide improved estimators under the quadratic loss tr(Σ −1 −Σ −1 ) 2 .To this end, a new and general Stein-Haff identity is derived for the high-dimensional elliptically symmetric distribution setting.

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A New Class of Improved Estimators of a Multinormal Precision Matrix

Cited by 4 publications

References 4 publications

Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data

Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data

Estimation of the inverse scatter matrix for a scale mixture of Wishart matrices under Efron–Morris type losses

Estimation of the inverse scatter matrix of an elliptically symmetric distribution

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