Nonlinear function-on-function additive model with multiple predictor curves
نویسندگان
چکیده
We consider a nonlinear function-on-function additive regression model with multiple functional predictors. The forms of the nonlinear functions are unspecified, and offer great flexibility to model various relationships between the response curve and predictor curves. We clarify the identifiability issue of the model and identify the best decompositions of the nonlinear functions in the model in terms of prediction. To estimate this expansion, we solve a penalized functional generalized eigenvalue problem followed by a penalized least squares procedure. With the minimum prediction error of the proposed decomposition, our approach has good prediction accuracy. Our approach converts the estimation of three-dimensional nonlinear functions to the estimation of twoand one-dimensional functions, which considerably reduces computational costs. Asymptotic results are provided, and simulations and a real data application show that the proposed method has good predictive performance and is efficient in dimension reduction and computation.
منابع مشابه
Multiple solutions of the nonlinear reaction-diusion model with fractional reaction
The purpose of this letter is to revisit the nonlinear reaction-diusion modelin porous catalysts when reaction term is fractional function of the concen-tration distribution of the reactant. This model, which originates also in uidand solute transport in soft tissues and microvessels, has been recently givenanalytical solution in terms of Taylors series for dierent family of reactionterms. We a...
متن کاملThe 2-additive fuzzy Choquet integral-based TODIM method with improved score function under hesitant fuzzy environment
Recently, the TODIM$^1$(an acronym in Portuguese of interactive and multi-criteria decision making) method has attracted increasing attention and many researchers have extended it to deal with multiple attribute decision making (MADM) problems under different situations. However, none of them can be used to handle MADM problems with positive, independent, and negative interactions among attribu...
متن کاملبهکارگیری مدل جمعیتعمیمیافته در تعیین نوع ارتباط عوامل خطر رتینوپاتی در بیماران دیابتی شهر تهران
Background : One of the most important complications of diabetes, is diabetic retinopathy that causes the blindness of 10,000 people every year. Different researches have been done on retinopathy risk factors in diabetic patients. This study was carried out to check the type of relationship between retinopathy risk factors and the condition of temptation it with generalized additive models. T...
متن کاملContinuously Additive Models for Nonlinear Functional Regression
We introduce continuously additive models, which can be motivated as extensions of additive regression models with vector predictors to the case of infinite-dimensional predictors. This approach provides a class of flexible functional nonlinear regression models, where random predictor curves are coupled with scalar responses. In continuously additive modeling, integrals taken over a smooth sur...
متن کاملPartly parametric generalized additive model
In many scientific studies, the response variable bears a generalized nonlinear regression relationship with a certain covariate of interest, which may, however, be confounded by other covariates with unknown functional form. We propose a new class of models, the partly parametric generalized additive model (PPGAM) for doing generalized nonlinear regression with the confounding covariate effect...
متن کامل