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Title: Regression with correlated noise: Non-parametric approach Authors:  Paulo Serra - Eindhoven University of Technology (Netherlands) [presenting]
Tatyana Krivobokova - Georg-August-Universitaet Goettingen (Germany)
Francisco Rosales Marticorena - Universidad del Pacifico (Peru)
Abstract: Regression models, particularly of the ``signal+noise'' variant, play a central role in statistics and are a fundamental tool in many applied fields. Typically, the noise terms are assumed to be independent but this is often not realistic. Methods for selecting bandwidths/smoothing parameters for kernel/spline estimators can break down even if the correlation is mild. Two common approaches are to either ``robustify'' the criteria for selecting bandwidth/smoothing parameters, or making a parametric assumption on the noise. Unfortunately, both approaches are sensitive to misspecification. We will focus on a non-parametric approach using smoothing spline estimators. The spline parameters and correlation matrix are estimated via the empirical Bayes approach. The estimation of the correlation is rather non-trivial due to the unknown mean of the data. We will consider some implementation issues, and the asymptotics of the estimators. These asymptotics make explicit the influence of the correlation structure on the smoothing parameters of the penalised spline, and introduce some non-trivial constraints on the order of the splines. We will close with some numerical experiments where we compare our approach to competing estimators, and to a standard R procedure based on a (parametric) assumption on the noise structure.