Abstract
Comparisons of best linear unbiased estimators with some other prominent estimators have been carried out over the last six decades since the ground breaking work of Lloyd [13]; see Arnold et al. [1] and David and Nagaraja [9] for elaborate details in this regard. Recently, Pitman closeness comparison of order statistics as estimators for population parameters, such as medians and quantiles, and their applications have been carried out by Balakrishnan et al. [3–5, 7]. In this paper, we discuss the Pitman closest estimators based on convex linear combinations of two contiguous order statistics, which sheds additional insight with regard to the estimation of the population median in the case of even sample sizes. We finally demonstrate the proposed method for the uniform, exponential, power function and Pareto distributions.
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Acknowledgments
The authors thank the editors, Drs. Pankaj Choudhary, Chaitra H. Nagaraja and Tony Ng, for their kind invitation to present this paper for the volume. Our sincere thanks go to an anonymous reviewer whose valuable comments and suggestions on an earlier version of this manuscript led to this significantly improved version. We also take this opportunity to congratulate Dr. H.N. Nagaraja for his accomplishments so far and hopefully for many more productive years in the future!
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Balakrishnan, N., Davies, K.F., Keating, J.P., Mason, R.L. (2015). Pitman Closest Estimators Based on Convex Linear Combinations of Two Contiguous Order Statistics. In: Choudhary, P., Nagaraja, C., Ng, H. (eds) Ordered Data Analysis, Modeling and Health Research Methods. Springer Proceedings in Mathematics & Statistics, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-319-25433-3_2
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DOI: https://doi.org/10.1007/978-3-319-25433-3_2
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