Skip to main content
SpringerLink
Log in

Percentile estimators in location-scale parameter families under absolute loss

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

Estimators of percentiles of location-scale parameter families are optimized based on median unbiasedness and absolute risk. Median unbiased estimators and minimum absolute risk estimators are shown to exist within a class of equivariant estimators and depend upon medians of two completely specified distributions. This work extends earlier findings to a larger class of equivariant estimators. These estimators are illustrated in the normal and exponential distributions.

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

  • Balakrishnan N, Cohen AC (1991) Order statistics and inference: estimation methods. Academic Press, San Diego

    MATH  Google Scholar 

  • Basu D (1956) The concept of asymptotic efficiency. Sankhyā 17: 193–196

    MATH  Google Scholar 

  • Chakraborti S, Li J (2007) Confidence interval estimation of a normal percentile. Am Stat 61: 331–336

    Article  MathSciNet  Google Scholar 

  • Datta GS, Ghosh M (1988) Minimum risk equivariant estimators of percentiles in location-scale families of distributions. Calcutta Stat Assoc Bull 37: 201–207

    MATH  MathSciNet  Google Scholar 

  • Dyer DD, Keating JP, Hensley OH (1977) Comparison of point estimators of normal percentiles. Commun Stat Simul Comput B6: 269–283

    Article  MathSciNet  Google Scholar 

  • Epstein B, Sobel M (1954) Some theorems relevant to life testing from an exponential distribution. Ann Math Stat 25: 373–381

    Article  MATH  MathSciNet  Google Scholar 

  • Ghosh M, Sen PK (1989) Median unbiasedness and Pitman closeness. J Am Stat Assoc 84: 1089–1091

    Article  MATH  MathSciNet  Google Scholar 

  • Keating JP (1983) Estimators of percentiles based on absolute loss. Commun Stat Theory Methods A12: 441–447

    MathSciNet  Google Scholar 

  • Keating JP, Mason RL, Sen PK (1993) Pitman’s measure of closeness. Society for Industrial and Applied Mathematics, Philadelphia

    MATH  Google Scholar 

  • Keating JP, Tripathi RC (1985) Percentiles, estimation of, Encyclopedia of statistical sciences, vol VI. Wiley, New York, pp 668–674

  • Lawless JF (2003) Statistical models and methods for lifetime data, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Lehmann EL (1983) Theory of point estimation. Springer, New York

    MATH  Google Scholar 

  • Mann N, Schafer RE, Singpurwalla ND (1974) Methods for statistical analysis of reliability and life data. Wiley, New York

    MATH  Google Scholar 

  • Mann N (1969) Optimum estimators for linear functions of location and scale paramters. Ann Math Stat 40: 2149–2155

    Article  MATH  Google Scholar 

  • Patil GP, Rao CR (1977) The weighted distributions: a survey of their applications. In: Krishnaiah PR (eds) Applications in statistics. North Holland, Amsterdam, pp 383–405

    Google Scholar 

  • Rukhin AL, Strawderman WE (1982) Estimating a quantile of an exponential distribution. J Am Stat Assoc 77: 159–162

    Article  MATH  MathSciNet  Google Scholar 

  • Sukhatme PV (1937) Tests of significance for samples of the χ2 population with two degrees of freedom. Ann Eugen 8: 52–56

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of Texas at San Antonio, San Antonio, TX, 78249-0704, USA

    J. P. Keating

  2. Southwest Research Institute, San Antonio, TX, 78228-0510, USA

    R. L. Mason

  3. McMaster University, Hamilton, ON, L8S 4K1, Canada

    N. Balakrishnan

Authors
  1. J. P. Keating
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. L. Mason
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Balakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. P. Keating.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Keating, J.P., Mason, R.L. & Balakrishnan, N. Percentile estimators in location-scale parameter families under absolute loss. Metrika 72, 351–367 (2010). https://doi.org/10.1007/s00184-009-0257-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-009-0257-0

Keywords

Search

Navigation