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New insights on goodness-of-fit tests for ranked set samples

Author

Listed:
  • M. Mahdizadeh

    (Hakim Sabzevari University)

  • Ehsan Zamanzade

    (University of Isfahan
    Institute for Research in Fundamental Sciences (IPM))

Abstract

Ranked set sampling (RSS) utilizes auxiliary information on the variable of interest so as to assist the experimenter in acquiring an informative sample from the population. The resulting sample has a stratified structure, and often improves statistical inference with respect to the simple random sample of comparable size. In RSS literature, there are some goodness-of-fit tests based on the empirical estimators of the in-stratum cumulative distribution functions (CDFs). Motivated by the fact that the in-stratum CDFs in RSS can be expressed as functions of the population CDF, some new tests are developed and their asymptotic properties are explored. An extensive simulation study is performed to evaluate properties of different testing procedures when the parent distribution is normal. It turns out that the proposed tests can be considerably more powerful than their contenders in many situations. An application in the context of fishery is also provided.

Suggested Citation

  • M. Mahdizadeh & Ehsan Zamanzade, 2022. "New insights on goodness-of-fit tests for ranked set samples," Statistical Papers, Springer, vol. 63(6), pages 1777-1799, December.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:6:d:10.1007_s00362-021-01284-7
    DOI: 10.1007/s00362-021-01284-7
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    References listed on IDEAS

    as
    1. Frey, Jesse & Ozturk, Omer & Deshpande, Jayant V., 2007. "Nonparametric Tests for Perfect Judgment Rankings," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 708-717, June.
    2. 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.
    3. Lutz Dümbgen & Ehsan Zamanzade, 2020. "Inference on a distribution function from ranked set samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 157-185, February.
    4. Jesse Frey & Timothy G. Feeman, 2017. "Efficiency comparisons for partially rank-ordered set sampling," Statistical Papers, Springer, vol. 58(4), pages 1149-1163, December.
    5. M. Mahdizadeh & Ehsan Zamanzade, 2021. "Smooth estimation of the area under the ROC curve in multistage ranked set sampling," Statistical Papers, Springer, vol. 62(4), pages 1753-1776, August.
    6. Fligner, Michael A. & MacEachern, Steven N., 2006. "Nonparametric Two-Sample Methods for Ranked-Set Sample Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1107-1118, September.
    7. Steven N. MacEachern & Ömer Öztürk & Douglas A. Wolfe & Gregory V. Stark, 2002. "A new ranked set sample estimator of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 177-188, May.
    8. M. Mahdizadeh & Ehsan Zamanzade, 2020. "Estimating asymptotic variance of M-estimators in ranked set sampling," Computational Statistics, Springer, vol. 35(4), pages 1785-1803, December.
    Full references (including those not matched with items on IDEAS)

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