Nonparametric shape constraints, such as monotonicity, convexity or log-concavity, offer statisticians the potential of freedom from restrictive parametric assumptions, while still permitting fully automatic procedures. In this sense, they combine the best of both the parametric and nonparametric worlds. Fundamental statistical problems such as density estimation and regression problems will be treated, along with more exotic questions related to, for example, semiparametric inference.
Inference under shape constraints is a core area of statistical theory and methodology, but the methods often involve challenging optimisation problems and have important applications in many areas, including biology and econometrics.