Sampling designs dependent on sample parameters of auxiliary variables (Q2634586)

This short monograph of 78 pages ``represents a synthesis of contributions on sampling designs that are dependent on sample moments or the order statistics of auxiliary variables''. The introductory chapter presents basic sampling designs and estimators including the Horvitz-Thompson estimator (11 pp.). The 14 pages long second chapter discusses well-known sampling designs dependent on sample moments of the auxiliary variable. These include Lahiri-Midzuno-Sen (LMS), Sampford and Singh and Srivastava's schemes as well as the author's extensions to designs with probability proportional to generalized variance. Chapter 3 (18 pp.) is mostly the author's work describing sampling designs based on order statistics such as design probability proportional to a function of one order statistic, functions of two and three order statistics. The algebra gets more complicated in the latter designs as the author says: ``But, in this case the expressions for inclusion probabilities become very complicated.'' (p. 48). An immediate thought leads to designs based on ranked set sampling which could be interesting and perhaps worth exploring. The final Chapter 4 deals with a simulation study to compare the efficiency of 13 strategies (28 pp.) including the author's. While in Chapter 3, the author gives practical situations where functions of one order statistic, two order statistics etc. are used, in the fourth chapter when introducing strategies dependent on a sum of order statistics, no such illustrations are given. A few references at the end of each chapter are given. Language wise, it is not difficult to follow the text. However, a careful reading of the draft could have been arranged by the publisher. Some notations are not standard, but on a re-reading, one can easily make out what the author's notations stand for. Research scholars in this field will find this brief useful.