Multiscale Approximation in Function Spaces

• Activity Number: 227
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Laurie Davies*+
• Companies: University of Duisburg Essen
• Keywords: Multiscale, ; regularization ; non-parametric regression, ; image analysis ; inverse problems

Abstract

Presenter. Laurie Davies

Abstract: Given the standard model for non-parametric regression and a data set the problem is to produce functions such that data generated under the model using such a function will look like the real data. The precise definition of look like requires the residuals to satisfy a set of linear inequalties which are multiscale in nature. These guarantee that the residuals look like Gaussian white noise. The set of all adequate functions is very large and includes for example all functions which interpolate the data making the residuals zero. Interest however centres on the simplest such functions, for example the ones with the minimum number of local extreme values, or the minimum number of intervals of convexity and concavity, or the smoothest ones in termes of derivatives. This gives rise to optimization problems such as large linear and dynamic programming problems. Examples will be given from non-parametric regression, image analysis and financial time series.