Title: A new scale estimator based on the kernel density estimator with ranked set sampling
Authors: Hikaru Yamaguchi - Tokyo University of Science (Japan) [presenting]
Hidetoshi Murakami - Tokyo University of Science (Japan)
Abstract: The ranked set sampling (RSS) is a cost-efficient alternative to the simple random sampling (SRS) in situations where the exact measurements of sample units are difficult or expensive to obtain but (judgment) ranking of them according to the variable of interest is relatively easy and cheap. We investigate the point estimation and interval estimation of scale by using RSS data for two independent random variables with unknown probability distributions. Kernel density estimation is one of nonparametric probability density estimation methods and is used in various fields. In the literature, the estimation of the probability $P(X<Y)$ for the location parameter based on the kernel density estimator is proposed and its analog in RSS is also discussed. We propose a new scale estimator based on the kernel density estimation with RSS and show that the suggested estimator is superior to that of SRS. In addition, we show the consistency and the asymptotic unbiasedness of the proposed estimator. In point estimation, the performance of estimators is compared by mean square error. A bootstrap method based on RSS is used to construct the nonparametric confidence intervals and the performance of the proposed estimator is evaluated by Monte Carlo simulation.