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Quadratic Programming and Penalised Regression

by Andrew D. A. C. Smith

Quadratic programming is a versatile tool for calculating estimates in penalised regression. It can be used to produce estimates based on L1 roughness penalties, as in total variation denoising. In particular, it can calculate estimates when the roughness penalty is the total variation of a derivative of the estimate. Combining two roughness penalties, the total variation and total variation of the third derivative, results in an estimate with continuous second derivative but controls the number of spurious local extreme values. A multiresolution criterion may be included in a quadratic program to achieve local smoothing without having to specify smoothing parameters.

Full text of the paper (pdf), which is accepted for publication in the Communications in Statistics: Theory and Methods special issue commemorating the 17th European Young Statisticians' Meeting, Lisbon 2011. doi: 10.1080/03610926.2012.732177