This monograph is the first book-length exposition of ranked set sampling. But, the subject matter is by no means new. The original notion of ranked set sampling, though not the technical term, was proposed by McIntyre in 1952. It was buried in the literature for quite a while. Its value was only re-discovered in recent years because of its cost-effective nature. Now, ranked set sampling has attracted practical interest in application areas such as agriculture, forestry, ecological and environmental science, and medical studies etc .. The theoretical foundations of the method has also been developed considerably, particularly during the last 15 years or so. A systematic exposition of the subject becomes necessary. This book covers every development of RSS since the birth of the original idea. Statistical inferences based on RSS are investigated from the originally intended estimation of a population mean to many more complicated pro­ cedures such as the inferences on smooth-function-of-means, quantiles and density functions, the distribution-free tests and regression analyses. Various variants of the original RSS scheme are explored, including RSS with imper­ fect judgment ranking or ranking by concomitant variables, adaptive RSS, multi-layer RSS and a variety of unbalanced RSS with certain optimalities.

Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration.

This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern­ ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense.