Statistica Sinica

Zehua Chen

Abstract:When observations are costly or time-consuming but the ranking of the observations without actual measurement can be done relatively easily, ranked-set sampling (RSS) can be employed instead of simple random sampling (SRS) to gain more information. In this article, we deal with RSS under multi-parameter parametric families. It is proved that the Fisher information matrix of an RSS sample is the sum of its counterpart of an SRS sample and an additional positive definite matrix. This insures that the maximum likelihood estimates (MLE) based on RSS are always more efficient than their counterparts based on SRS. The effect of certain features of the underlying distribution such as skewness and kurtosis on the relative efficiency of the MLE is also investigated. Some other aspects of RSS are discussed as well.

Key words and phrases:Asymptotic relative efficiency, confidence interval, Fisher information, maximum likelihood estimation, ranked-set sampling.