Functional adaptive group lasso with its non-asymptotic bounds

초록

In this article, we develop theories and methods for functional predictor selection of multivariate functional data within the context of a scalar-on-function regression problem. Current existing methods either lack valid theoretical validation or require overly strong assumptions that are not verifiable from the data. To address these limitations and understand the necessary conditions for sparse methods of multivariate functional data, we introduce new statistical concepts, an extended correlation operator and a standardized regression operator for multivariate functional data. We then derive a new penalty scheme under this framework and establish non-asymptotic bounds under more relaxed and reasonable assumptions, identifying conditions for selection and estimation consistency. Simulation results and real data application to human brain datasets indicate that our method outperforms existing methods. It is anticipated that the proposed theoretical framework and penalty scheme can enhance numerous other penalized methods for functional data analysis.

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