18 Induced order statistics: Theory and applications

Publisher Summary This chapter discusses the theory and applications related to the induced order statistics. Recently a systematic study of the induced order statistics, their ranks, their extremes and their partial sums are undertaken. The chapter assumes that X and Y are two numerical characteristics defined for each individual in a population. Induced order statistics arise naturally in the context of selection where individuals ought to be selected by their ranks in respect of Y , but are selected by their ranks in a related variate X due to unavailability of Y at the time of selection. Induced order statistics are also useful in regression analysis, especially when the observations are subject to a type II censoring scheme with respect to the dependent variable, or when the regression function at a given quantile of the predictor variable is of interest.

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