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A new ranked set sample estimator of variance. (English) Zbl 1067.62032

Summary: We develop an unbiased estimator of the variance of a population based on a ranked set sample. We show that this new estimator is better than estimating the variance based on a simple random sample and more efficient than the estimator based on a ranked set sample proposed by S. L. Stokes [Biometrika 36, 35–42 (1980; Zbl 0425.62023)]. Also, a test to determine the effectiveness of the judgment ordering process is proposed.

MSC:

62G05 Nonparametric estimation
62G30 Order statistics; empirical distribution functions

Citations:

Zbl 0425.62023

Software:

SDaA
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References:

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[9] Stokes, Estimation of variance using judgment ordered ranked set samples, Biometrics 36 pp 35– (1980) · Zbl 0425.62023 · doi:10.2307/2530493
[10] Stokes, Characterization of a ranked-set sample with application to estimating distribution functions, J. Am. Statist. Ass. 83 pp 374– (1988) · Zbl 0644.62050 · doi:10.1080/01621459.1988.10478607
[11] Takahasi, On unbiased estimates of the population mean based on the sample stratified by means of ordering, Ann. Inst. Statist. Math. 20 pp 1– (1968) · Zbl 0157.47702 · doi:10.1007/BF02911622
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