Skip to main content
SpringerLink
Log in

On Fisher information inequalities in the presence of nuisance parameters

  • General
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

The existence of a generalized Fisher information matrix for a vector parameter of interest is established for the case where nuisance parameters are present under general conditions. A matrix inequality is established for the information in an estimating function for the vector parameter of interest. It is shown that this inequality leads to a sharper lower bound for the variance matrix of unbiased estimators, for any set of functionally independent functions of parameters of interest, than the lower bound provided by the Cramér-Rao inequality in terms of the full parameter.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bhapkar, V. P. (1972). On a measure of efficiency of an estimating equation,Sankhyā Ser. A,34, 467–472.

    Google Scholar 

  • Bhapkar, V. P. (1989). Conditioning on ancillary statistics and loss of information in the presence of nuisance parameters,J. Statist. Plann. Inference,21, 139–160.

    Google Scholar 

  • Bhapkar, V. P. (1990). Conditioning, marginalization and Fisher information functions,Probability Statistics and Design of Experiments (ed. R. R. Bahadur), Wiley Eastern Limited, New Delhi.

    Google Scholar 

  • Bhapkar, V. P. (1991). Loss of information in the presence of nuisance parameters and partial sufficiency,J. Statist. Plann. Inference,28, 185–203.

    Google Scholar 

  • Chandrasekar, B. and Kale, B. K. (1984). Unbiased statistical estimation functions for parameters in presence of nuisance parameters,J. Statist. Plann. Inference,9, 45–54.

    Google Scholar 

  • Cox, D. R. and Reid, N. (1987). Parameter orthogonality and approximate conditional inference,J. Roy. Statist. Soc. Ser. B,49, 1–39.

    Google Scholar 

  • Ferreira, P. E. (1982). Multiparametric estimating equations,Ann. Inst. Statist. Math.,34, 423–431.

    Google Scholar 

  • Friedman, A. (1982).Foundations of Modern Analysis, Dover, New York.

    Google Scholar 

  • Godambe, V. P. (1960). An optimum property of a regular maximum likelihood estimation,Ann. Math. Statist.,31, 1208–1211.

    Google Scholar 

  • Godambe, V. P. (1984). On ancillarity and Fisher information in the presence of nuisance parameter,Biometrika,71, 626–629.

    Google Scholar 

  • Kale, B. K. (1962). An extension of the Cramér-Rao inequality for statistical estimation functions,Skand. Aktuarietidskr.,45, 80–89.

    Google Scholar 

  • Rao, C. R. (1965).Linear Statistical Inference, Wiley, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Kentucky, 817 Patterson Office Tower, 40506-0027, Lexington, KY, U.S.A.

    Vasant P. Bhapkar & Cidambi Srinivasan

Authors
  1. Vasant P. Bhapkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cidambi Srinivasan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported in part by NSF Grant MCS-8806233.

Supported in part by NSF Grants RII-8610671, ATM-9108177 and DMS-9204380.

About this article

Cite this article

Bhapkar, V.P., Srinivasan, C. On Fisher information inequalities in the presence of nuisance parameters. Ann Inst Stat Math 46, 593–604 (1994). https://doi.org/10.1007/BF00773520

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00773520

Key words and phrases

Search

Navigation