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.

Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling

“…Double RSS-DRSS (Al-Saleh and Al-Kadiri [25]) is a more efficient, but also more expensive, version of RSS that ranks a larger number of sets in two ordering stages, whereas paired RSS-PRSS (Hossain and Muttlak [26]) is a less expensive option that ranks a smaller number of units. A recently proposed sampling scheme can be found for different probability distributions including [27][28][29][30][31][32][33][34].…”

Efficient Estimation of the Generalized Quasi-Lindley Distribution Parameters under Ranked Set Sampling and Applications

“…Pedroso et al [30] considered the RSS to estimate the parameters of the twoparameter Birnbaum-Saunders distribution, and Akgul et al [31] used the same RSS in system reliability estimation for generalized inverse Lindley distribution. (see also Taconeli and Bonat [32] for some estimation methods based on the RSS). For more details on parameter estimation, the readers are referred to Stokes [33]; Dey et al [34]; Khamnei and Mayan [35]; and Al-Saleh and Al-Hadhrami [36].…”