## Abstract

Suppose that n independent observations are drawn from a multivariate normal distribution N_{p} (μ, Σ) with both mean vector μ and covariance matrix Σ unknown. We consider the problem of estimating the precision matrix Σ^{- 1} under the squared loss L (over(Σ, ^)^{- 1}, Σ^{- 1}) = tr (over(Σ, ^)^{- 1} Σ - I_{p})^{2}. It is well known that the best lower triangular equivariant estimator of Σ^{- 1} is minimax. In this paper, by using the information in the sample mean on Σ^{- 1}, we construct a new class of improved estimators over the best lower triangular equivariant minimax estimator of Σ^{- 1} for p = 2. Our improved estimators are in the class of lower-triangular scale equivariant estimators and the method used is similar to that of Stein [1964. Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean. Ann. Inst. Statist. Math. 16, 155-160.].

Original language | English |
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Pages (from-to) | 127-134 |

Number of pages | 8 |

Journal | Statistics and Probability Letters |

Volume | 78 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Feb 2008 |

Externally published | Yes |

## Keywords

- Best lower triangular equivariant minimax estimator
- Bivariate normal distribution
- Inadmissibility
- Precision matrix
- The squared loss