Projecting Statistical Functionals This monograph presents a general method of establishing explicit solutions to classical problems of calculating the best lower and upper mean variance bounds on various statistical functionals over various nonparametric families of distributions. The functionals include quantiles standard and conditional expectations of record and order statistics from independent and dependent samples and a variety of their combinations important in statistics and reliability. The following families of distributions are taken into account: arbitrary symmetric symmetric unimodal and U shaped ones distributions with monotone density and failure rate and monotone density and failure rate on the average distributions. The method is based on determining projections of the functionals onto properly chosen convex cones in functional Hilbert spaces. It allows us to explicitly point out the distributions which attain the bounds. The book is addressed to students researchers and practitioners in statistics and applied probability. Most of the results have been established recently and a significant part of them has not been published yet. Numerous open problems are stated in the text