FUNCTIONAL SUFFICIENT DIMENSION REDUCTION THROUGH AVERAGE FRECHET DERIVATIVES.

ABSTRACT: Sufficient dimension reduction (SDR) embodies a family of methods that aim for reduction of dimensionality without loss of information in a regression setting. In this article, we propose a new method for nonparametric function-on-function SDR, where both the response and the predictor are a function. We first develop the notions of functional central mean subspace and functional central subspace, which form the population targets of our functional SDR. We then introduce an average Fréchet derivative estimator, which extends the gradient of the regression function to the operator level and enables us to develop estimators for our functional dimension reduction spaces. We show the resulting functional SDR estimators are unbiased and exhaustive, and more importantly, without imposing any dis

SUBMITTER: Lee KY 

PROVIDER: S-EPMC10085580 | biostudies-literature | 2022 Apr

REPOSITORIES: biostudies-literature