New Bootstrap Methods for the Hypothesis Tests of the Population Mean in Ranked Set Sampling

Year 2020, Volume: 24 Issue: 1, 64 - 71, 20.04.2020

Nurdan Yeniay Koçer , Yaprak Arzu Özdemir , Fikri Gökpınar

https://doi.org/10.19113/sdufenbed.554741

Cited By: 1

Abstract

Ranked Set Sampling is an efficient technique when it is difficult to measure sampling units in respect to cost or time. Although this technique can be used for every sample sizes, the small sample sizes are preferred for better ranking. However, when the sample sizes are small, it is very difficult to obtain distribution of the statistic for the statistical inference such as hypothesis test. In this case, resampling techniques like bootstrap can be used to construct pseudo distribution of the statistics. In this study, the bootstrap methods for hypothesis test about population mean under ranked set sampling is given. A simulation study is also performed to examine the performance of these methods.

Keywords

Ranked set sampling, Bootstrap, Powers of test, Monte Carlo simulation

Sıralı Küme Örneklemesinde Yığın Ortalamasına İlişkin Hipotez Testi İçin Yeni Bootstrap Metotları

Abstract

Sıralı küme örneklemesi, örnekleme birimlerini ölçmenin maliyet ve zaman bakımından zor olduğu durumda kullanılan etkin bir örnekleme tekniğidir. Bu teknik, her çapta örnek için kullanılabilir olmasına rağmen sıralama hatasını minimuma indirmek için küçük örnek çaplarında daha çok tercih edilir. Ancak, hipotez testi gibi istatistiksel çıkarsama yaparken küçük örnek çapı durumunda, istatistiğin kesin ya da asimptotik dağılımını elde etmek oldukça zordur. Bu durumda, istatistiğin yapay dağılımını elde etmek için Bootstrap gibi yeniden örnekleme teknikleri kullanılabilir. Bu çalışmada, sıralı küme örneklemesi altında yığın ortalamasına ilişkin hipotez testi için Bootstrap metotları verilmiştir. Ayrıca, verilen metotların performansını değerlendirmek için simülasyon çalışması yapılmıştır.

Keywords

Sıralı küme örneklemesi, Bootstrap, Testin gücü, Monte Carlo simülasyonu

References

• [1] McIntyre, G. A. 1952. A method of unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research, vol. 3: 385-390.
• [2] Takahasi, K. and Wakimoto, K. 1968. On Unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of The Institude of Statistical Mathematics, 2: 249-255.
• [3] Dell, D. R. and Clutter, J. L. 1972. Ranked set sampling theory with order statistics background. Biometrics, vol. 28: 545-555.
• [4] Shen, W. H. 1994. On estimation of a log-normal mean using a ranked set sample. Sankhya, 54(B): 323-333.
• [5] Bhoj, D. S. and Ahsanullah, M. 1996. Estimation of parameters of the generalized geometric distribution using ranked set sampling. Biometrics, 52: 685-694.
• [6] Abu-Dayyeh, W., Assrhani, A. and Ibrahim, K. 2011. Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling. Statistical Papers, 54(1): 1-19.
• [7] Albatineh, A. N., Kibria, B. M. G., Wilcox , M. L. and Zogheib, B. 2014. Confidence interval estimation for the population coefficient of variation using ranked set sampling: a simulation study. Journal of Applied Statistics, 41: 733-751.
• [8] Özturk, Ö. 2015. Estimation of a finite population mean and total using population ranks of sample units. Journal of Agricultural, Biological, and Environmental Statistics, 21(1): 181–202.
• [9] Özturk, Ö. and Demirel, N. 2016. Estimation of population variance from multiranker ranked set sampling designs. Communications in Statistics - Simulation and Computation, 45(10): 3568-3583.
• [10] Muttlak, H. A. and Abu-Dayyeh, W. 1998. Testing some hypothese about the normal distribution using ranked set samples: a more powerful test. Journal of Information & Optimization Sciences, 19(1): 1–11.
• [11] Özdemir, Y. A. and Gökpınar, F. 2006. Hypothesis testing for the population mean using unbiased ranked set sampling designs. International Journal of Pure and Applied Mathematics, 31: 501-513.
• [12] Özdemir, Y. A., Ebegil, M. and Gökpınar, F. 2016. A test statistic based on ranked set sampling for two normal means. Journal Communications in Statistics - Simulation and Computation, 46(10): 8077-8085.
• [13] Efron, B. 1979. Bootstrap methods: Another look at Jackknife. Institute Of Mathematical Statistics, 7: 1-26.
• [14] Hui, T. P., Modarres, R. and Zheng, G. 2005. Bootstrap confidence interval estimation of mean via ranked set sampling linear regression. Journal of the Statistical Computaion and Simulation. vol. 75 Issue: 7 Pages:543-553.
• [15] Modarres, R., Hui, T.P. and Zheng, G. 2006. Resampling methods for ranked set samples. Computational Statistics and Data Analysis, 51: 1039-1050.
• [16] MacEachern, S. N., Öztürk, Ö., Wolfe, D.A. and Stark, G. V. 2002. A new ranked set sample estimator of variance. Journal of the Royal Statistical Society Statistical Methodology. Series B. vol.64 Issue:2 Pages: 177-188.