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A General Projection Framwork For Constrained Smoothing, E Mammen, J S. Marron, B A. Turlach, M P. Wand

Faculty of Engineering and Information Sciences - Papers: Part A

There are a wide array of smoothing methods available for finding structure in data. A general framework is developed which shows that many of these can be viewed as a projection of the data, with respect to appropriate norms. The underlying vector space is an unusually large product space, which allows inclusion of a wide range of smoothers in our setup (including many methods not typically considered to be projections). We give several applications of this simple geometric interpretation of smoothing. A major payoff is the natural and computationally frugal incorporation of constraints. Our point of view also motivates new …