PROJECTION METHOD FOR MOMENT BOUNDS ON ORDER-STATISTICS FROM RESTRICTED FAMILIES .1. DEPENDENT CASE

We present a method of projections onto convex cones for establishing the sharp bounds in terms of the first two moments for the expectation s of L-estimates based on samples from restricted families. In this pa rt, we consider the case of possibly dependent identically distributed parent random variables. For the classes of decreasing failure probab ility, DFR, and symmetric unimodal marginal distributions, we first de termine parametric subclasses which contain the distributions attainin g the extreme expectations for all L-estimates. Then we derive the bou nds for single order statistics. The results provide some new characte rizations of uniform and exponential distributions. (C) 1996 Academic Press. Inc.