Shape-Constrained Estimation Using Nonnegative Splines
a general framework that treats estimation problems in a unified manner
applications of the approach
- compute optimal spline estimators for regression, density estimation, and arrival rate estimation problems
- can handle multiple simultaneous shape constraints
- based on a characterization of nonnegative polynomials that leads to semdefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problem.
- these formulation extend and generalize previous approaches in the literature, including those with piecewise linear and B-spline estimators
- also consider a simpler approach in which nonnegative coefficients in a nonnegative basis