Kagan, Abram ; Landsman, Zinoviy ; Rao, C. Radhakrishna
(2007)
*Sub- and superadditivity a la Carlen of matrices related to the fisher information*
Journal of Statistical Planning and Inference, 137
(1).
pp. 291-298.
ISSN 0378-3758

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.jspi.2005.07.011

## Abstract

Let Z=(Z^{(1)},Z^{(2)}) be an s-variate random vector partitioned into r- and q-variate subvectors whose distribution depends on an s-variate location parameter θ=(θ^{(1)},θ^{(2)}) partitioned in the same way as Z. For the s×s matrix I of Fisher information on θ contained in Z and r×r and q×q matrices I_{1} and I_{2} of Fisher information on θ^{(1)} and θ^{(2)} in Z^{(1)} and Z^{(2)}, it is proved that trace(I^{-1}) ≤ trace(I^{-1}_{1})+trace(I^{-1}_{2}). The inequality is similar to Carlen's superadditivity but has a different statistical meaning: it is a large sample version of an inequality for the covariance matrices of Pitman estimators. If the distribution of Z depends also on an m-variate nuisance parameter η (of a general nature) and I,I^{(1)} and I^{(2)} are the efficient matrices of information on θ,θ^{(1)},θ^{(2)} in Z,Z^{(1)} and Z^{(2)}, respectively, then trace(I) ≥ trace(I^{1})+trace(I^{1}).

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Efficient Matrix of Fisher Information; Location Parameter; Pitman Estimator |

ID Code: | 58141 |

Deposited On: | 31 Aug 2011 12:37 |

Last Modified: | 31 Aug 2011 12:37 |

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