Shape-Constrained Regression using Sum of Squares Polynomials

We consider the problem of fitting a polynomial function to a set of data points, each data point consisting of a feature vector and a response variable. In contrast to standard polynomial regression, we require that the polynomial regressor satisfy shape constraints, such as monotonicity, Lipschitz-continuity, or convexity. We show how to use semidefinite programming … Read more

Consistency of robust portfolio estimators

It is a matter of common knowledge that traditional Markowitz optimization based on sample means and covariances performs poorly in practice. For this reason, diverse attempts were made to improve performance of portfolio optimization. In this paper, we investigate three popular portfolio selection models built upon classical mean-variance theory. The first model is an extension … Read more

Statistical inference of multistage stochastic programming problems

We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal value of the true problem. However, in order for such lower bound to be consistent one needs to employ the conditional sampling procedure. … Read more