Journal of Hebei University(Natural Science Edition) >

2020 , Vol. 40 >Issue 3: 225 - 231

DOI: https://doi.org/10.3969/j.issn.1000-1565.2020.03.001

Wilcoxon signed-rank test based on ranked set sampling with unequal samples

  • DONG Xiaofang ,
  • ZHANG Liangyong ,
  • WANG Zhijun
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  • School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China

Received date: 2019-12-04

  Online published: 2020-05-25

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Abstract

In order to test the symmetric point of an infinite population, a Wilcoxon signed-rank test statistic based on ranked set sampling with unequal samples is constructed. Its distribution is shown to be symmetric and distribution-free under null hypothesis. The asymptotic normality of the new test statistic is proved, and its Pitman efficiency factor is given. The calculated results of Pitman asymptotic relative efficiencies show that the new test is superior to the signed-rank tests under simple random sampling and ranked set sampling.

Key words： ranked set sampling; signed-rank test; Pitman efficiency; simple random sampling

Cite this article

DONG Xiaofang , ZHANG Liangyong , WANG Zhijun . Wilcoxon signed-rank test based on ranked set sampling with unequal samples[J]. Journal of Hebei University(Natural Science Edition), 2020 , 40(3) : 225 -231 . DOI: 10.3969/j.issn.1000-1565.2020.03.001

References

[1] MCINTYRE G A. A method for unbiased selective sampling using ranked sets[J]. Australian Journal of Agricultural Research, 1952, 3: 385-390. DOI: 10.1071/ar9520385.
[2] RISCH N, ZHANG H. Extreme discordant sib pairs for mapping quantitative trait loci in humans [J]. Science, 1995, 268(5217): 1584-1589. DOI: 10.1126/science.7777857.
[3] MEHMOOD R, RIAZ M, DOES R. Quality quandaries: on the application of different ranked set sampling schemes[J]. Quality Engineering, 2014, 26(3): 370-378. DOI: 10.1080/08982112.2014.903971.
[4] WANG X L, LIM J, STOKES L. Using ranked set sampling with cluster randomized designs for improved inference on treatment effects[J]. Journal of the American Statistical Association, 2016, 111(516): 1576-1590. DOI: 10.1080/01621459.2015.1093946.
[5] ZAMANZADE E, MAHDIZADEH M. Estimating the population proportion in pair ranked set sampling with application to air quality monitoring[J]. Journal of Applied Statistics, 2018, 45(3): 1-12. DOI: 10.1080/02664763.2017.1279596.
[6] BHOJ D S. Ranked set sampling with unequal samples [J]. Biometrics, 2001, 57(3): 957-962. DOI: 102307/3068438.
[7] GEMAYEL N M, STASNY E A, WOLFE D A. Optimal ranked set sampling estimation based on medians from multiple set sizes[J]. Journal of Nonparametric Statistics, 2010, 22(4): 517-527. DOI: 10.1080/1048525090330517.
[8] DONG X F, ZHANG L Y, LI F Q. Estimation of reliability for exponential distributions using ranked set sampling with unequal samples[J]. Quality Technology & Quantitative Management, 2013, 10(3): 319-328. DOI: 10.1080/16843703.2013.11673417.
[9] 张良勇, 徐兴忠, 董晓芳. 基于非均等排序集抽样的符号检验[J]. 北京理工大学学报(自然科学版), 2015, 35(6): 639-643. DOI: 10.15918/j.tbit1001-0645.2015.06.018.
[10] RANDLES R H, WOLFE D A. Introduction to the theory of nonparametric statistics[M]. New York: John Wiley & Sons, 1979.
[11] BOHN L L. A ranked set sample signed-rank statistic[J]. Journal of Nonparametric Statistics, 1998, 9(3): 295-306. DOI: 10.1080/10485259808832747.
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