Skip to main content
SpringerLink
Log in

Fisher information in order statistics and their concomitants in bivariate censored samples

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

We evaluate the Fisher information (FI) contained in a collection of order statistics and their concomitants from a bivariate random sample. Special attention is given to Type II censored samples. We present a general decomposition result and recurrence relations that are useful in finding the FI in all types of censored samples. We also obtain some asymptotic results for the FI. For the bivariate normal parent, we obtain explicit and asymptotic expressions for the elements of the FI matrix for Type II censored samples. We discuss implications of our findings on inference on the bivariate normal parameters, especially on the correlation.

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

  • Abo-Eleneen ZA, Nagaraja HN (2002) Fisher information in an order statistic and its concomitant. Ann Inst Stat Math 54:667–680

    Article  MATH  MathSciNet  Google Scholar 

  • Al-Saleh MF, Zheng G (2002) Estimation of bivariate characteristics using ranked set sampling. Aust New Zealand J Stat 44:221–232

    Article  MATH  MathSciNet  Google Scholar 

  • Arnold BC, Balakrishnan N (1989) Relations, bounds and approximations for order statistics. Lecture notes in statistics 53. Springer, New York

    MATH  Google Scholar 

  • Cox DR, Hinkley DV (1974) Theoretical statistics. Chapman & Hall, London

    MATH  Google Scholar 

  • David HA, Nagaraja HN (1998) Concomitants of order statistics. In: Balakrishnan N, Rao CR (eds) Handbook of statistics, 16. Elsevier, Amsterdam, pp 487–513

    Google Scholar 

  • David HA, Nagaraja HN (2003) Order statistics, 3rd edn. Wiley, New York

    MATH  Google Scholar 

  • Escobar LA, Meeker WQ (1998) Fisher information matrices with censoring, truncation, and explanatory variables. Stat Sin 8:221–237

    MATH  MathSciNet  Google Scholar 

  • Gastwirth JA (1965) Asymptotically most powerful rank tests for the two-sample problem with censored data. Ann Math Stat 36:1243–1247

    Article  MathSciNet  Google Scholar 

  • Harell FE, Sen PK (1979) Statistical inference for censored bivariate normal distributions based on induced order statistics. Biometrika 66:293–298

    Article  MathSciNet  Google Scholar 

  • Harter LH, Balakrishnan N (1996) Handbook of tables for the use of order statistics in estimation. CRC Press, New York

    MATH  Google Scholar 

  • Lehmann EL, Casella G (1998) Theory of point estimation, 2nd edn. Springer, New York

    MATH  Google Scholar 

  • Mehrotra KG, Johnson RA, Bhattacharyya GK (1979) Exact Fisher information for censored samples and the extended hazard rate functions. Commun Stat Theor Meth 15:1493–1510

    Article  MathSciNet  Google Scholar 

  • Mosteller F (1946) On some useful inefficient statistics. Ann Math Stat 17:377–408

    Article  MathSciNet  Google Scholar 

  • Park S (1996) Fisher information in order statistics. J Amer Stat Assoc 91:385–390

    Article  MATH  Google Scholar 

  • Park S (2003) On the asymptotic Fisher information in order statistics. Metrika 57:71–80

    Article  MathSciNet  Google Scholar 

  • Spruill NL, Gastwirth JL (1982) On the estimation of the correlation coefficient from grouped data. J Am Stat Assoc 77:614–620

    Article  MATH  MathSciNet  Google Scholar 

  • Stokes SL (1980) Inference on the correlation coefficient in bivariate normal populations from ranked set samples. J Am Stat Assoc 75:989–995

    Article  MATH  MathSciNet  Google Scholar 

  • Takahashi H, Sugiura N (1989) The rate of convergence of Fisher information for type II censored sample. J Jpn Stat Soc 19:139–144

    MATH  MathSciNet  Google Scholar 

  • Teichroew D (1956) Tables of expected values of order statistics and products of order statistics for samples of size twenty and less from the normal distribution. Ann Math Stat 27:410–426

    Article  MathSciNet  Google Scholar 

  • Zheng G (2000) On the rate of convergence of Fisher information in multiple type II censored data. J Jpn Stat Soc 30:197–204

    MATH  Google Scholar 

  • Zheng G, Gastwirth JL (2000) Where is the Fisher information in an ordered sample?. Stat Sin 10:1267–1280

    MATH  MathSciNet  Google Scholar 

  • Zheng G, Park S (2004) On the Fisher information in multiply censored and progressively censored data. Commun Stat Theor Meth 33:1821–1835

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Ohio State University, Columbus, OH, 43210-1247, USA

    H. N. Nagaraja

  2. Faculty of Computers and Informatics, Zagazig University, Zagazig, Egypt

    Z. A. Abo-Eleneen

Authors
  1. H. N. Nagaraja
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. A. Abo-Eleneen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. N. Nagaraja.

Additional information

The first author’s research was supported in part by National Institutes of Health, USA, Grant # M01 RR00034 and the second author’s research was supported by a training grant from the Egyptian government

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nagaraja, H.N., Abo-Eleneen, Z.A. Fisher information in order statistics and their concomitants in bivariate censored samples. Metrika 67, 327–347 (2008). https://doi.org/10.1007/s00184-007-0136-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-007-0136-5

Keywords

Search

Navigation