Functional interaction-based nonlinear models with application to multiplatform genomics data.

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Functional regression models scalar outcomes based on functional predictors.
• Limited research exists on incorporating scalar exposures that interact with functional covariates.

Purpose of the Study:

• To develop novel functional regression models accounting for scalar exposure-functional covariate interactions.
• To propose robust estimation procedures for these models, handling noisy or sparse functional data.

Main Methods:

• Introduced two new functional regression models.
• Developed two novel estimation procedures for model parameters.
• Extended methods to generalized exponential family responses and computed standard errors.

Main Results:

• The proposed methods effectively handle noisy and sparsely observed functional covariates.
• Statistical inference and hypothesis testing are enabled through computed standard errors.
• Simulations demonstrated the performance of the estimators compared to existing methods.

Conclusions:

• The novel functional regression models provide a framework for analyzing complex interactions.
• The developed estimation procedures are flexible and applicable to various response types.
• The methods are validated through simulation and a real-world data example.