Weak Convergence of Some Quantile Processes Arising in Progressively Censored Tests

Abstract

For progressive censoring schemes pertaining to a general class of (parametric as well as nonparametric) testing situations, one encounters a (partial) sequence of linear combinations of functions of order statistics where the coefficients are themselves stochastic variables. Weak convergence of such a quantile process to an appropriate Gaussian function is studied here, and the same is incorporated in the formulation of suitable (time-) sequential tests based on these quantile processes.