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Optimal unbiased estimation of some population central moments

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  • Mariano Ruiz Espejo
  • Miguel Delgado Pineda
  • Saralees Nadarajah

Abstract

In this paper, we have treated the problem of estimating some population central moments under distribution-free setting. Uniformly minimum variance unbiased estimators for some population central moments have been derived. Some examples of unbiased estimators of central moments have been given under various sampling designs such as simple random sampling with replacement (srsr) or without replacement (srs), probability proportional to size with replacement (ppsr) and probability graduated variable proportional to size without replacement (pgvps). An optimal unbiased estimator of the third population central moment is proposed and extended to some real situations. Some optimal unbiased estimators of the fourth population central moment are given. Several optimal unbiased estimators of the variance of the “sample quasivariance estimator” are identified. Finally, computer programs in R implementing all of the estimators are given. Copyright Sapienza Università di Roma 2013

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  • Mariano Ruiz Espejo & Miguel Delgado Pineda & Saralees Nadarajah, 2013. "Optimal unbiased estimation of some population central moments," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 39-62, June.
    • Handle: RePEc:spr:metron:v:71:y:2013:i:1:p:39-62
    DOI: 10.1007/s40300-013-0006-z
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    1. Cem Kadilar & Yesim Unyazici & Hulya Cingi, 2009. "Ratio estimator for the population mean using ranked set sampling," Statistical Papers, Springer, vol. 50(2), pages 301-309, March.
    2. Housila Singh & Rajesh Tailor & Sarjinder Singh & Jong-Min Kim, 2008. "A modified estimator of population mean using power transformation," Statistical Papers, Springer, vol. 49(1), pages 37-58, March.
    3. Guiso, Luigi & Jappelli, Tullio & Pistaferri, Luigi, 2002. "An Empirical Analysis of Earnings and Employment Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 241-253, April.
    4. Campbell Harvey & John Liechty & Merrill Liechty & Peter Muller, 2010. "Portfolio selection with higher moments," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 469-485.
    5. Erickson, Timothy & Whited, Toni M., 2002. "Two-Step Gmm Estimation Of The Errors-In-Variables Model Using High-Order Moments," Econometric Theory, Cambridge University Press, vol. 18(3), pages 776-799, June.
    6. Ke-Hai Yuan & Robert Jennrich, 2000. "Estimating Equations with Nuisance Parameters: Theory and Applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 343-350, June.
    7. Annaliisa Kankainen & Sara Taskinen & Hannu Oja, 2007. "Tests of multinormality based on location vectors and scatter matrices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(3), pages 357-379, November.
    8. Wu, Jianhong & Su, Weihua, 2010. "Estimation of moments for linear panel data models with potential existence of time effects," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1933-1939, December.
    9. Sarjinder Singh, 2001. "Generalized Calibration Approach for Estimating Variance in Survey Sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 404-417, June.
    10. Ishwaran H. & Takahara G., 2002. "Independent and Identically Distributed Monte Carlo Algorithms for Semiparametric Linear Mixed Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1154-1166, December.
    11. Ping Wu & Li Xing Zhu, 2010. "An Orthogonality‐Based Estimation of Moments for Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 253-263, June.
    12. Angela Montanari & Cinzia Viroli, 2010. "A skew-normal factor model for the analysis of student satisfaction towards university courses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 473-487.
    13. Mariano Espejo & Mercedes Espejo, 1992. "Equilibrated strategy for population variance estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 1(1), pages 79-91, December.
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    Cited by:

    1. Mariano Ruiz Espejo, 2015. "Modern survey sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(4), pages 917-918, April.

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