Sub- and superadditivity à la Carlen of matrices related to the Fisher information

Abram Kagan, Zinoviy Landsman, C. Radhakrishna Rao

Research output: Contribution to journalArticlepeer-review


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 I1 and I2 of Fisher information on θ(1) and θ(2) in Z(1) and Z(2), it is proved that trace (I- 1) ≤ trace (I1- 1) + trace (I2- 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 languageEnglish
Pages (from-to)291-298
Number of pages8
JournalJournal of Statistical Planning and Inference
Issue number1
StatePublished - 1 Jan 2007


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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