Enforcing shape constraints on a probability density estimate using an additive adjustment curve

ABSTRACT

A method is proposed for shape-constrained density estimation under a variety of constraints, including but not limited to unimodality, monotonicity, symmetry, and constraints on the number of inflection points of the density or its derivative. The method involves computing an adjustment curve that is used to bring a pre-existing pilot estimate into conformance with the specified shape restrictions. The pilot estimate may be obtained using any preferred estimator, and the optimal adjustment can be computed using fast, readily-available quadratic programming routines. This makes the proposed procedure generic and easy to implement.