Recent Advances on Functional Additive Regression
Conference paper
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Abstract
We introduce a flexible approach to approximate the regression function in the case of a functional predictor and a scalar response. Following the Projection Pursuit Regression principle, we derive an additive decomposition which exploits the most interesting projections of the prediction variable to explain the response. The goodness of our procedure is illustrated from theoretical and pratical points of view.
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References
- 1.Ferraty, F., Goia, A., Salinelli, E., Vieu, P.: Additive Functional Regression based on Predictive Directions. WP 13/10, Dipartimento di Scienze Economiche e Metodi Quantitativi, Universit`a del Piemonte Orientale A. Avogadro (2010)Google Scholar
- 2.Ferraty, F., Vieu, P.: Nonparametric functional data analysis. Springer, New York (2006) 3. Friedman, J.H., Stuetzle, W.: Projection Pursuit Regression. J. Am. Stat. Assoc. 76, 817–823 (1981)Google Scholar
- 3.Hall, P. (1989). On projection Pursuit Regression. Ann. Stat. 17 (2), 573–588 (1989)MATHGoogle Scholar
- 4.James, G.M., Silverman, B.W.: Functional Adaptive Model Estimation. J. Am. Stat. Assoc. 100 (470), 565–576 (2005)MathSciNetMATHCrossRefGoogle Scholar
- 5.M¨uller, H.G., Yao, F.: Functional Additive Model. J. Am. Stat. Assoc. 103 (484), 1534–1544 (2008)Google Scholar
- 6.Ramsay, J.O., Silverman, B.W.:Functional Data Analysis (Second Edition). Springer Verlag, New York (2005)Google Scholar
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