CDF estimation in multistage pair ranked set sampling

Year 2022, Volume: 51 Issue: 6, 1768 - 1779, 01.12.2022

Mahdi Mahdizadeh , Ehsan Zamanzade

https://doi.org/10.15672/hujms.1031349

Abstract

Multistage pair ranked set sampling (MSPRSS) is a rank-based design that improves statistical inference with respect to simple random sampling of the same size. It is applicable when exact measurement is difficult, but judgment raking of the potential sample units can be done fairly accurately and easily. The ranking is usually performed based on personal judgment or a concomitant variable, and need not be totally free of errors. This article deals with estimating the cumulative distribution function in MSPRSS. The proposed estimator is theoretically compared with its contenders in the literature. The findings are supported by numerical evidence from simulation, and real data in the context of body fat analysis. Finally, a cost analysis is performed to show the advantage of the estimator.

Keywords

CDF estimation, cost efficiency, judgment ranking

References

• [1] M.F. Al-Saleh and A.I. Al-Omari, Multistage ranked set sampling, J. Statist. Plann. Inference 102 (2), 273-286, 2002.
• [2] M.F. Al-Saleh and M.J. Samuh, On multistage ranked set sampling for distribution and median estimation, Comput. Statist. Data Anal. 52 (4), 2066-2078, 2008.
• [3] C.N. Bouza-Herrera and A.I. Al-Omari, Ranked Set Sampling, 65 Years Improving the Accuracy in Data Gathering, Academic Press, 2019.
• [4] T.R. Dell and J.L. Clutter, Ranked set sampling theory with order statistics background, Biometrics 28 (2), 545-555, 1972.
• [5] J. Frey, Bounds on the efficiency of unbalanced ranked-set sampling, Comm. Statist. Theory Methods 49 (1), 243-256, 2020.
• [6] J. Frey and T.G. Feeman, Efficiency comparisons for partially rank-ordered set sampling, Statist. Papers 58 (4), 1149-1163, 2017.
• [7] J. Frey and T.G. Feeman, Finding the maximum efficiency for multistage ranked-set sampling, Comm. Statist. Theory Methods 47 (17), 4131-4141, 2018.
• [8] N.M. Gemayel, E.A. Stasny, J.A. Tackett and D.A. Wolfe, Ranked set sampling: An auditing application, Rev. Quant. Finance Account. 39 (4), 413-422, 2012.
• [9] M. Mahdizadeh and E. Strzalkowska-Kominiak, Resampling based inference for a distribution function using censored ranked set samples, Comput. Statist. 32 (4), 1285-1308, 2017.
• [10] M. Mahdizadeh and E. Zamanzade, Reliability estimation in multistage ranked set sampling, REVSTAT 15 (4), 565-581, 2017.
• [11] M. Mahdizadeh and E. Zamanzade, Dynamic reliability estimation in a rank-based design, Probab. Math. Statist. 39 (1), 1-18, 2019.
• [12] M. Mahdizadeh and E. Zamanzade, Efficient body fat estimation using multistage pair ranked set sampling, Stat. Methods Med. Res. 28 (1), 223-234, 2019.
• [13] M. Mahdizadeh and E. Zamanzade, Estimating asymptotic variance of M-estimators in ranked set sampling, Comput. Statist. 35 (4), 1785-1803, 2020.
• [14] M. Mahdizadeh and E. Zamanzade, Estimation of a symmetric distribution function in multistage ranked set sampling, Statist. Papers 61 (2), 851-867, 2020.
• [15] M. Mahdizadeh and E. Zamanzade, Smooth estimation of the area under the ROC curve in multistage ranked set sampling, Statist. Papers 62 (4), 1753-1776, 2021.
• [16] G.A. McIntyre, A method of unbiased selective sampling using ranked sets, Aust. J. Agric. Res. 3 (4), 385-390, 1952.
• [17] H.A. Muttlak, Pair rank set sampling, Biom. J. 38 (7), 879-885, 1996.
• [18] E. Strzalkowska-Kominiak and M. Mahdizadeh, On the Kaplan-Meier estimator based on ranked set samples, J. Stat. Comput. Simul. 84 (12), 2577-2591, 2014.
• [19] X. Wang, J. Lim and L. Stokes, Using ranked set sampling with cluster randomized designs for improved inference on treatment effects, J. Amer. Statist. Assoc. 111 (516), 1576-1590, 2016.