关键词: 函数型响应变量, 非线性可加模型, 变量选择

Abstract:

In this paper, we consider variable selection for the nonlinear additive model whose response variable and covariate are both functional data. First, we construct an F test statistic based on the functional distance correlation and sort the functional distance correlation coefficients of the covariates and residuals. Also, the independent F test is conducted for the covariates and residuals corresponding to the maximum correlation coefficients, and the qualified new variables are included in the model. Second, the contribution of each new variable in the model is evaluated to determine whether the new variable should eventually be included in the model. The procedure separates the selection process from the model estimation by picking the candidates using a model-free measurement, which can reduce the dimension of the covariates in the regression. At the same time, the residual error can be used to obtain the relevant information of the model during the iteration process to improve the accuracy of variable selection. Finally, the performance of the proposed variable selection procedure is assessed with Monte Carlo simulation studies. We further demonstrate the proposed procedure with a dataset of the energy consumption of appliances.

Key words: Functional Response Variables, Nonlinear Additive Model, Variable Selection