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Change-point Estimation and Inference in Nonparametric Regression Using Different Regularization Concepts

Tuesday, November 5, 2013 - 11:00
Matus Maciak, Department of Mathematical and Statistical Sciences, University of Alberta
Room 4192, Earth Sciences Building (2207 Main Mall)

Classical regression techniques require a smoothness assumption to be satisfied. It makes the theoretical justification easier and the model more straightforward to interpret. In many situations however, statisticians need to deal with more complex dependence structures where the underlying functional form is non-smooth, or even discontinuous. Such models are in statistics referred to as change-point models as locations where the smoothness (continuity) assumption is not satisfied are commonly said to be change-points. Unfortunately, many existing methods require a
prior knowledge for the location of change-points in a model, which can be quite limiting in practical situations.

We will propose a new approach to change-point estimation in regression: the main advantage of our method is that it introduces a fully data-driven approach with no requirement on prior knowledge for change-point locations. It combines nonparametric regression estimation with different concepts of an L1-norm regularization.

Different alternatives are proposed, a proper statistical inference is discussed and theoretical results are derived. Finite sample performance is investigated using simulated data and real examples as well.

Edmonton, AB – 08.10.2013