On the performance of estimation methods under ranked set sampling

Abstract

Maximum likelihood estimation (MLE) applied to ranked set sampling (RSS) designs is usually based on the assumption of perfect ranking. However, it may suffers of lack of efficiency when ranking errors are present. The main goal of this article is to investigate the performance of six alternative estimation methods to MLE for parameter estimation under RSS. We carry out an extensive simulation study and measure the performance of the maximum product of spacings, ordinary and weighted least-squares, Cramér-von-Mises, Anderson–Darling and right-tail Anderson–Darling estimators, along with the maximum likelihood estimators, through the Kullback–Leibler divergence from the true and estimated probability density functions. Our simulation study considered eight continuous probability distributions, six sample sizes and six levels of correlation between the interest and concomitant variables. In general, our results show that the Anderson–Darling method outperforms its competitors and that the maximum likelihood estimators strongly depends on perfect ranking for accurate estimation. Finally, we present an illustrative example using a data set concerning the percent of body fat. R code is available in the supplementary material.

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Acknowledgements

The authors thank the Editor and the Reviewers for their valuable comments on an earlier version of this manuscript.

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Correspondence to Cesar Augusto Taconeli.

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Taconeli, C.A., Bonat, W.H. On the performance of estimation methods under ranked set sampling. Comput Stat 35, 1805–1826 (2020). https://doi.org/10.1007/s00180-020-00953-9

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Keywords

  • Anderson–Darling statistic
  • Kullback–Leibler divergence
  • Maximum likelihood estimation
  • Monte Carlo simulation
  • Statistical efficiency