Additive nonlinear functional concurrent model

Journal of Computational and Graphical Statistics

et al. 2018

Self Cite

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself, as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. The estimation/inferential procedure accommodates realistic scenarios, such as correlated error structure as well as sparse and/or irregular designs. We investigate our methodology in finite sample size through simulations and two real data applications. Supplementary Material for this article is available online.

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Out-of-sample Predictionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Additive Function-on-Function Regression

Kim

Staicu

Journal of Computational and Graphical Statistics

et al. 2018

Self Cite

“…A more general additive model with multiple functional covariates is

Y_{i} ((), t) = μ ((), t) + true {false\sum}_{q = 1}^{Q} F_{q} ({}, X_{i q} ((), t), t) + ε_{i} ((), t),

where μ (⋅) is an unknown intercept function, and F q (⋅,⋅), q = 1, …, Q are unknown smooth functions. Such models are considered by Kim et al and by Scheipl et al as a part of a more general framework.…”

Section: Nonparametric Concurrent Modelsmentioning

confidence: 99%

Nonparametric functional concurrent regression models

WIREs Computational Stats

2017

Self Cite

Function-on-function regression refers to the situation where both independent and dependent variables in a regression model are of functional nature. Functional concurrent regression is a specific type of function-on-function regression that relates the response function at a specific point to the covariate value at that point and the point itself. Standard functional concurrent models are linear (a linear combination of the covariates is used), and often criticized due to their linearity assumption and lack of flexibility. This gives rise to nonparametric functional concurrent regression that models the response function at a specific point using a multivariate nonparametric function of both the point and the covariate value at that point. Such models allow for much more flexibility and predictive accuracy, especially when the underlying relationship is nonlinear. In the past decade, several methods have been proposed to perform estimation, prediction and inference in the nonparametric concurrent models using various methods such as spline smoothing, Gaussian process regression and local polynomial kernel regression. Such models have been shown to be useful tools in functional regression as well as stepping stone for further development.

Variable selection in nonparametric functional concurrent regression

Ghosal

2021

Can J Statistics

Self Cite

We develop a new method for variable selection in nonparametric functional concurrent regression. The commonly used functional linear concurrent model (FLCM) is far too restrictive in assuming linearity of the covariate effects, which is not necessarily true in many real‐world applications. The nonparametric functional concurrent model (NPFCM), on the other hand, is much more flexible and can capture complex dynamic relationships present between the response and the covariates. We extend the classically used variable selection methods, e.g., group LASSO, group SCAD and group MCP, to perform variable selection in NPFCM. We show via numerical simulations that the proposed variable selection method with the non‐convex penalties can identify the true functional predictors with minimal false‐positive rate and negligible false‐negative rate. The proposed method also provides better out‐of‐sample prediction accuracy compared to the FLCM in the presence of nonlinear effects of the functional predictors. The proposed method's application is demonstrated by identifying the influential predictor variables in two real data studies: a dietary calcium absorption study, and some bike‐sharing data.