Generalized additive models for functional data

The aim of this paper is to extend the ideas of generalized additive models for multivariate data (with known or unknown link function) to functional data covariates. The proposed algorithm is a modified version of the local scoring and backfitting algorithms that allows for the nonparametric estimation of the link function. This algorithm would be applied to predict a binary response example.

[1]  Frédéric Ferraty,et al.  Cross-validated estimations in the single-functional index model , 2008 .

[2]  Frédéric Ferraty,et al.  Additive prediction and boosting for functional data , 2009, Comput. Stat. Data Anal..

[3]  Maria L. Rizzo,et al.  Measuring and testing dependence by correlation of distances , 2007, 0803.4101.

[4]  Joel L. Horowitz Semiparametric Methods in Econometrics: Lecture Notes in Statistics 131 , 1998 .

[5]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[6]  P. Hall,et al.  Single and multiple index functional regression models with nonparametric link , 2011, 1211.5018.

[7]  J. Horowitz Semiparametric Methods in Econometrics , 2011 .

[8]  Gareth M. James Generalized linear models with functional predictors , 2002 .

[9]  Joel L. Horowitz,et al.  NONPARAMETRIC ESTIMATION OF A GENERALIZED ADDITIVE MODEL WITH AN UNKNOWN LINK FUNCTION , 2001 .

[10]  H. Cardot,et al.  Estimation in generalized linear models for functional data via penalized likelihood , 2005 .

[11]  James O. Ramsay,et al.  Functional Data Analysis , 2005 .

[12]  Fang Yao,et al.  Functional Additive Models , 2008 .

[13]  Javier Roca-Pardiñas,et al.  Predicting binary time series of SO2 using generalized additive models with unknown link function , 2004 .

[14]  Philippe Vieu,et al.  Semi-functional partial linear regression , 2006 .

[15]  Aldo Goia,et al.  A functional linear model for time series prediction with exogenous variables , 2012 .

[16]  Ana M. Aguilera,et al.  Functional PLS logit regression model , 2007, Comput. Stat. Data Anal..

[17]  B. Silverman,et al.  Functional Data Analysis , 1997 .

[18]  Ulrich Stadtmüller,et al.  Generalized functional linear models , 2005 .

[19]  Manuel Febrero-Bande,et al.  Statistical Computing in Functional Data Analysis: The R Package fda.usc , 2012 .

[20]  R. Tibshirani,et al.  Linear Smoothers and Additive Models , 1989 .

[21]  Gareth M. James,et al.  Functional Adaptive Model Estimation , 2005 .

[22]  Gareth M. James,et al.  Functional additive regression , 2015, 1510.04064.

[23]  A. M. Aguilera,et al.  Principal component estimation of functional logistic regression: discussion of two different approaches , 2004 .

[24]  Frédéric Ferraty,et al.  Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics) , 2006 .