基于非均等排序集抽样的Wilcoxon符号秩检验

doi:10.3969/j.issn.1000-1565.2020.03.001

河北大学学报(自然科学版) ›› 2020, Vol. 40 ›› Issue (3): 225-231.DOI: 10.3969/j.issn.1000-1565.2020.03.001

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基于非均等排序集抽样的Wilcoxon符号秩检验

董晓芳,张良勇,王志军

收稿日期:2019-12-04 出版日期:2020-05-25 发布日期:2020-05-25
作者简介:董晓芳(1981—),女,河北永年人,河北经贸大学副教授,博士,主要从事非参数统计和抽样技术方向的研究. E-mail:dxfys81@126.com
基金资助:
国家自然科学基金资助项目(11801134);河北经贸大学科学研究项目(2015KYQ03;2016KYQ08)

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

DONG Xiaofang, ZHANG Liangyong, WANG Zhijun

School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China

Received:2019-12-04 Online:2020-05-25 Published:2020-05-25

摘要/Abstract

摘要： 为了检验未知总体的对称点,建立了非均等排序集抽样下的Wilcoxon符号秩检验统计量,证明了在原假设下其分布具有对称性和适应任意分布性,证明了新检验统计量的渐近正态性,并给出新检验的Pitman效率因子.Pitman渐近相对效率的计算结果表明,新检验优于简单随机抽样下和均等排序集抽样下的符号秩检验.

关键词: 排序集抽样, 符号秩检验, Pitman效率, 简单随机抽样

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

中图分类号:

O212.7

董晓芳,张良勇,王志军. 基于非均等排序集抽样的Wilcoxon符号秩检验[J]. 河北大学学报(自然科学版), 2020, 40(3): 225-231.

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.

参考文献

[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.

基于非均等排序集抽样的Wilcoxon符号秩检验

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

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