## 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_{2}^{- 1}). 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 over(I, ^), over(I, ^) ^{(1)} and over(I, ^) ^{(2)} are the efficient matrices of information on θ, θ^{(1)}, θ^{(2)} in Z, Z^{(1)} and Z^{(2)}, respectively, then trace (over(I, ^)) ≥ trace (over(I, ^) ^{(1)}) + trace (over(I, ^) ^{(2)}).

Original language | English |
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Pages (from-to) | 291-298 |

Number of pages | 8 |

Journal | Journal of Statistical Planning and Inference |

Volume | 137 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2007 |

## Keywords

- Efficient matrix of Fisher information
- Location parameter
- Pitman estimator

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics