Adaptive DWO Estimator of a Regression Function
2004 (English)In: Proceedings of the 2004 IFAC Symposium on Nonlinear Control Systems, 2004Conference paper (Refereed)
We address a problem of non-parametric estimation of an unknown regression function f : [-1/2, 1/2] → R at a fixed point x0 € (-1/2, 1/2) on the basis of observations (xi, yi), i = 1,..,n such that yi = f(xi) + ei, where ei ~ N(0, σ2) is unobservable, Gaussian i.i.d. random noise and xi € [-1/2, 1/2] are given design points. Recently, the Direct Weight Optimization (DWO) method has been proposed to solve a problem of such kind. The properties of the method have been studied for the case when the unknown function f is continuously differentiable with Lipschitz constant L. The minimax optimality and adaptivity with respect to the design have been established for the resulting estimator. However, in order to implement the approach, both L and σ are to be known. The subject of the submission is the study of an adaptive version of DWO estimator which uses a data-driven choice of the method parameter L.
Place, publisher, year, edition, pages
Non-parametric regression, Estimators, Adaptive algorithms, Mean-square error, Quadratic programming
IdentifiersURN: urn:nbn:se:liu:diva-90331OAI: oai:DiVA.org:liu-90331DiVA: diva2:613583
2004 IFAC Symposium on Nonlinear Control Systems, Stuttgart, Germany, September, 2004