Functional linear and single-index models: A unified approach via Gaussian Stein identity

Understand

Functional linear and single-index models are core regression methods in functional data analysis and are widely used for performing regression in a wide range of applications when the covariates are random functions coupled with scalar responses.

• In the existing literature, however, the construction of associated estimators and the study of their theoretical properties is invariably carried out on a case-by-case basis for specific models under consideration.
• In this work, assuming the predictors are Gaussian processes, we provide a unified methodological and theoretical framework for estimating the index in functional linear, and its direction in single-index models.
• In the latter case, the proposed approach does not require the specification of the link function.