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Ozturk, Omer

Nonparametric maximum-likelihood estimation of within-set ranking errors in ranked set sampling. (English) Zbl 1203.62043

J. Nonparametric Stat. 22, No. 7, 823-840 (2010).
Summary: A distribution-free statistical inference for the quality of within-set judgement ranking information is developed for ranked set samples. The judgement ranking information is modelled through the L. L. Bohn and D. A. Wolfe (BW) model [J. Am. Stat. Assoc. 87, No. 418, 552–561 (1992; Zbl 0781.62051); ibid. 89, No. 425, 168–176 (1994; Zbl 0800.62251)]. The cumulative distribution function and the parameters of BW model are estimated by maximising nonparametric likelihood functions. A missing data model is introduced to construct an efficient computational algorithm. The advantages of the new estimators are that they require essentially no assumption on the underlying distribution function, which provides an estimate of the quality of within-set ranking information, and that they lead to a valid statistical inference even under imperfect ranking. The proposed estimators are applied to a water flow data set to estimate judgement ranking information and underlying distribution function.

Cited in 13 Documents

MSC:

62G05 Nonparametric estimation
62G07 Density estimation
62G30 Order statistics; empirical distribution functions
62D99 Statistical sampling theory and related topics
65C60 Computational problems in statistics (MSC2010)
62P12 Applications of statistics to environmental and related topics

Keywords:

imperfect ranking; ranking models; mixture models; EM algorithm; ranked set sampling; judgement ranking; nonparametric likelihood; missing data models

Citations:

Zbl 0781.62051; Zbl 0800.62251
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References:

[1] DOI: 10.1016/S0167-7152(99)00206-0 · Zbl 0949.62042 · doi:10.1016/S0167-7152(99)00206-0
[2] DOI: 10.1016/j.jspi.2005.08.050 · Zbl 1294.62018 · doi:10.1016/j.jspi.2005.08.050
[3] DOI: 10.1080/02664769723431 · doi:10.1080/02664769723431
[4] DOI: 10.2307/2290290 · Zbl 0781.62051 · doi:10.2307/2290290
[5] DOI: 10.2307/2291213 · Zbl 0800.62251 · doi:10.2307/2291213
[6] Chen Z., Sankhyā, Ser. A 62 pp 178– (2000)
[7] DOI: 10.2307/2556166 · Zbl 1193.62047 · doi:10.2307/2556166
[8] DOI: 10.1198/016214506000000410 · Zbl 1120.62314 · doi:10.1198/016214506000000410
[9] DOI: 10.1016/j.jspi.2006.02.013 · Zbl 1107.62010 · doi:10.1016/j.jspi.2006.02.013
[10] DOI: 10.2307/2290855 · Zbl 0803.62030 · doi:10.2307/2290855
[11] DOI: 10.1111/1467-9868.00331 · Zbl 1067.62032 · doi:10.1111/1467-9868.00331
[12] Murray R. A., Aspects of Applied Biology 57 pp 141– (2000)
[13] DOI: 10.1080/10485259908832760 · Zbl 0921.62054 · doi:10.1080/10485259908832760
[14] Ozturk O., Journal of Statistical Theory and Application 6 pp 360– (2007)
[15] DOI: 10.1002/cjs.5550360406 · Zbl 1166.62032 · doi:10.1002/cjs.5550360406
[16] Stokes S. L., Annals of the Institute of Statistical Mathematics 47 pp 465– (1995)
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