The Adjoint Projection Pursuit Regression

by Naihua Duan

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Regression analysis is one of the most useful tools in statistical analysis. Usually, regression analysis requires specifying the link function for the model. The popular link functions used widely include the linear link function, the logistic link function, and the probit link function. However, in many applications, the functional form and the link function might not be known precisely. Therefore, the usual regression analysis based on a specific link function might not perform well. This Note proposes a new regression method, the adjoint projection pursuit regression, which does not require specifying the link function in advance. The method is based on the nonparametric adjoint equation, and can be implemented using iteration of a sequence of modified least squares regression. The adjoint projection pursuit regression is shown to be consistent. A simulation study is given to illustrate this procedure.

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