IMS Grace Wahba Award and Lecture

Traditionally, we think of statistical methods as being divided into parametric approaches, which can be restrictive, but where estimation is typically straightforward (e.g. using maximum likelihood) and nonparametric methods, which are more flexible but often require careful choices of tuning parameters. Nonparametric inference under shape constraints sits somewhere in the middle, seeking in some ways the best of both worlds. I will give an introduction to the area, providing some history, recent developments and a future outlook.