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On multivariate order statistics. Application to ranked set sampling

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  • Arnold, Barry C.
  • Castillo, Enrique
  • María Sarabia, José

Abstract

Two new concepts of order statistics for multivariate samples are introduced. In one of the versions it turns out that not every multivariate order statistic is present in every sample. These order statistics have application in multivariate ranked set sampling and can be used to generate broad classes of multivariate densities in the sense of Jones. In this case the likelihood for the sample values and their corresponding ranks can be calculated based on the conditional density of a multivariate order statistics given its sample value, and such that its integral gives the probability for the multivariate order statistics under discussion to be observed. An alternative version of multivariate order statistics is also introduced, for which multivariate order statistics are always well defined and expressions for their marginal densities are derived. Since these multivariate order statistics are tailor made for multivariate ranked set sampling, their densities allow for parameter inference based on ranked set sampling. Some simulations show that both multivariate order statistics densities can be used with advantage with respect to simple random sampling.

Suggested Citation

  • Arnold, Barry C. & Castillo, Enrique & María Sarabia, José, 2009. "On multivariate order statistics. Application to ranked set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4555-4569, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4555-4569
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    References listed on IDEAS

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    5. Lucio Barabesi & Caterina Pisani, 2002. "Ranked Set Sampling for Replicated Sampling Designs," Biometrics, The International Biometric Society, vol. 58(3), pages 586-592, September.
    6. Bairamov, Ismihan, 2006. "Progressive Type II censored order statistics for multivariate observations," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 797-809, April.
    7. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    8. Lynne Stokes, 1995. "Parametric ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 465-482, September.
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