Sample average approximation is a popular approach to solving stochastic optimization problems. It has been widely observed that some form of robustification these problems often improves the out-of-sample performance solution estimators. In estimation problems, this improvement boils down trade-off between opposing effects bias and shrinkage. This paper aims characterize features more general ...

A sharp upper bound on the average distance of a graph depending on the order and the independence number is given. As a corollary we obtain the maximum average distance of a graph with given order and matching number. All extremal graphs are determined.