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Shrinkage Estimation Using Ranked Set Samples

  • Research Article - Mathematics
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Abstract

The purpose of this article is two-fold. First, we consider the ranked set sampling (RSS) estimation and testing hypothesis for the parameter of interest (population mean). Then, we suggest some alternative estimation strategies for the mean parameter based on shrinkage and pretest principles. Generally speaking, the shrinkage and pretest methods use the non-sample information (NSI) regarding that parameter of interest. In practice, NSI is readily available in the form of a realistic conjecture based on the experimenter’s knowledge and experience with the problem under consideration. It is advantageous to use NSI in the estimation process to construct improved estimation for the parameter of interest. In this contribution, the large sample properties of the suggested estimators will be assessed, both analytically and numerically. More importantly, a Monte Carlo simulation is conducted to investigate the relative performance of the estimators for moderate and large samples. For illustrative purposes, the proposed methodology is applied to a published data set.

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References

  1. Ahmed S.E., Gupta A.K., Khan S.M., Nicol C.: Simultaneous estimation of several interclass correlation coefficients. Ann. Inst. Stat. Math. 53, 354–369 (2000)

    Article  MathSciNet  Google Scholar 

  2. Ahmed S.E., Krzanowski W.J.: Biased estimation in a simple multivariate regression model. Comput. Stat. Data. Anal. 45, 689–696 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bancroft T.A.: On biases in estimation due to use of preliminary test of significance. Ann. Math. Stat. 15, 190–204 (1944)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bickel P.J., Doksum K.A.: Mathematical Statistics, vol. 1, 2nd edn. Prentice Hall, New Jersey (2001)

    Google Scholar 

  5. Chen Z., Bai Z., Sinha B.K.: Ranked Set Sampling. Theory and Applications. Springer, New York (2004)

    MATH  Google Scholar 

  6. Dell T.R., Clutter J.L.: Ranked set sampling theory with order statistics background. Biometrics. 28, 545–553 (1972)

    Article  MATH  Google Scholar 

  7. Judge G.G., Bock M.E.: The Statistical Implication of Pre-test and Stein-rule Estimators in Econometrics. North-Holland, Amsterdam (1978)

    Google Scholar 

  8. Kaur A., Patil G.P., Sinha B.K., Taillie C.: Ranked set sampling: an annotated bibliography. Environ. Ecol. Stat. 2, 25–54 (1995)

    Article  Google Scholar 

  9. McIntyre G.A.: A method for unbiased selective sampling, using, ranked sets Austral. J. Agric. Res. 3, 385–390 (1952)

    Article  Google Scholar 

  10. Muttlak H.A.: Median ranked set sampling. J. Appl. Stat. Sci. 6, 245–255 (1997)

    MATH  Google Scholar 

  11. Muttlak H.A., Al-Sabah W.S.: Statistical quality control based on ranked set sampling. J. Appl. Stat. 30, 1055–1078 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Muttlak H.A., Muttlak H.A.: Recent development in ranked set sampling. Pak. J. Stat. 16, 269–290 (2000)

    MathSciNet  MATH  Google Scholar 

  13. Patil, G.P.; Sinha, A.K.; Taillie, C.: Ranked set sampling. A Handbook of Statistics. vol. 12, pp. 167–200 (1994)

  14. Sakamoto Y., Yoshikazu T., Yoshida N.: Expansions of the coverage probabilities of prediction region based on a shrinkage estimator. Statistics. 38(5), 381–390 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sengupta S., Mukhuti S.: Unbiased estimation of P(X > Y) using ranked set sampling data. Statistics. 42(3), 223–230 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Stokes S.L.: Ranked set sampling with concomitant variables, Commun. Stat. Theory. Methods. A 6, 1207–1211 (1977)

    Article  Google Scholar 

  17. Takahasi K., Wakimoto K.: On the unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann. Inst. Stat. Math. 20, 1–31 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  18. Thompson J.R.: Some shrinkage techniques for estimating the mean. J. Am. Stat. Assoc. 63, 113–122 (1968)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    H. A. Muttlak

  2. Department of Mathematics and Statistics, University of Windsor, Windsor, ON, Canada

    S. E. Ahmed

  3. Department of Mathematics and Statistics, Zayed University, Dubai, UAE

    I. Rahimov

Authors
  1. H. A. Muttlak
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  2. S. E. Ahmed
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  3. I. Rahimov
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Corresponding author

Correspondence to H. A. Muttlak.

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Muttlak, H.A., Ahmed, S.E. & Rahimov, I. Shrinkage Estimation Using Ranked Set Samples. Arab J Sci Eng 36, 1125–1138 (2011). https://doi.org/10.1007/s13369-011-0106-0

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  • DOI: https://doi.org/10.1007/s13369-011-0106-0

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