Piecewise Convex Function Estimation: Representations, Duality and Model Selection
Methodology
2019-11-19 v1 Systems and Control
Signal Processing
Systems and Control
Statistics Theory
Data Analysis, Statistics and Probability
Statistics Theory
Abstract
We consider spline estimates which preserve prescribed piecewise convex properties of the unknown function. A robust version of the penalized likelihood is given and shown to correspond to a variable halfwidth kernel smoother where the halfwidth adaptively decreases in regions of rapid change of the unknown function. When the convexity change points are prescribed, we derive representation results and smoothness properties of the estimates. A dual formulation is given which reduces the estimate is reduced to a finite dimensional convex optimization in the dual space.
Keywords
Cite
@article{arxiv.1803.03901,
title = {Piecewise Convex Function Estimation: Representations, Duality and Model Selection},
author = {Kurt S. Riedel},
journal= {arXiv preprint arXiv:1803.03901},
year = {2019}
}