Abstract
In this article, we propose a generalized ranked set sampling (RSS) scheme, namely, varied L-RSS (VLRSS), for estimating the population mean. The VLRSS scheme encompasses several existing RSS schemes and helps in selecting more representative samples from the target population. It is shown that for a symmetric population, the mean estimator under VLRSS scheme is unbiased, and with reasonable assumptions, it is considerably better than the mean estimators based on RSS and LRSS schemes. Moreover, we also study the effect of imperfect ranking on the performance of VLRSS-based mean estimator. It turns out that, under an imperfect VLRSS scheme, the proposed estimator outperforms its counterparts. The proposed scheme is also illustrated with a case study using a real data set.
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References
Al-Naseer, A. D. 2007. L ranked set sampling: A generalization procedure for robust visual sampling. Commun. Stat. Simulation Comput., 36, 33–43.
Al-Omari, A. I., and M. Z. Raqab. 2013. Estimation of the population mean and median using truncation-based ranked set samples. J. Stat. Comput. Simulation, 83, 1453–1471.
Al-Saleh, M. F., and M. A. Al-Kadiri. 2000. Double-ranked set sampling. Stat. Probability Lett., 48, 205–212.
Chen, Z., and Y.-G. Wang. 2004. Efficient regression analysis with ranked-set sampling. Biometrics, 60, 997–1004.
Dell, T. R., and J. L. Clutter. 1972. Ranked set sampling theory with order statistics background. Biometrics, 28, 553–555.
Haq, A., J. Brown, E. Moltchanova, and A. I. Al-Omari. 2013. Partial ranked set sampling design. Environmetrics, 24, 201–207.
McIntyre, G. A. 1952. A method for unbiased selective sampling, using ranked sets. Austr. J. Agric. Res., 3, 385–390.
Muttlak, H. A. 1996. Pair rank set sampling. Biometrical J., 38, 879–885.
Muttlak, H. A. 1997. Median ranked set sampling. J. Appl. Stat. Sci., 6, 245–255.
Muttlak, H. A. 2003. Investigating the use of quartile ranked set samples for estimating the population mean. Appl. Math. Comput., 146, 437–443.
Platt, W. J., G. W. Evans, and S. L. Rathbun. 1988. The population dynamics of a long lived conifer (Pinus palustris). Am. Naturalist, 131, 491–525.
Samawi, H. M., W. Abu-Dayyeh, and M. S. Ahmed. 1996. Estimating the population mean using extreme ranked set sampling. Biometrical J., 38, 577–586.
Stokes, S. L. 1977. Ranked set sampling with concomitant variables. Commun. Stat. Theory Methods, 6, 1207–1211.
Takahasi, K., and K. Wakimoto. 1968. On unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann. Inst. Stat. Math., 20, 1–31.
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Haq, A., Brown, J., Moltchanova, E. et al. Varied L ranked set sampling scheme. J Stat Theory Pract 9, 741–767 (2015). https://doi.org/10.1080/15598608.2015.1008606
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DOI: https://doi.org/10.1080/15598608.2015.1008606