Much of statistics is concerned with estimating the values of uncertain quantities from available data, whether historical or experimental. Estimates are obtained by minimizing some error expression and fall therefore into a specially structured category of optimization. On the other hand, in applications of optimization more generally, the objective or constraint functions may depend on databases and require statistical methodology to be pinned down in a tractable form. This raises important issues in stochastic optimization in particular, where decisions can only shape the probability distributions of future "costs", and preferences in terms of so-called measures of risk must come in. It appears that such preferences should then influence the error expression used in estimation. Such interplay between optimization and statistics is leading to a greatly broadened theory of regression which relies heavily on convex analysis. A scheme called the fundamental quadrangle of risk unifies the ideas and suggests new lines of research.
