Nonparametric and shape restricted statistics
Nonparametric curve estimation is primarily concerned with understanding the structure (trend/pattern) in the data without making strong parametric assumptions on its form. Examples are nonparametric estimation procedures for a regression function, a failure rate, or a probability density. Shape restricted curve estimation by-passes the dependence on tuning parameters and seeks to develop estimates that are fully automated in situations where prior knowledge on the shape of the function is available. Such shape constraints arise naturally in numerous applications, e.g., utility/production functions are known to be non-decreasing and concave, distribution functions are known to be non-decreasing, sometimes regression curves or failure rates are known to be monotone/unimodal, etc.\(\)
