Abstract

Multivariate varying-coefficient models (MVCM) are popular statistical tools for analyzing the relationship between multiple responses and covariates. Nevertheless, estimating large numbers of coefficient functions is challenging, especially with a limited amount of samples. In this work, we propose a reduced-dimension model based on the Tucker decomposition, which unifies several existing models. In addition, sparse predictor effects, in the sense that only a few predictors are related to the responses, are exploited to achieve an interpretable model and sufficiently reduce the number of unknown functions to be estimated. All the above dimension-reduction and sparsity considerations are integrated into a penalized least squares problem on the constraint domain of 3rd-order tensors. To compute the proposed estimator, we propose a block updating algorithm with ADMM and manifold optimization. We also establish the oracle inequality for the prediction risk of the proposed estimator. A real data set from Framingham Heart Study is used to demonstrate the good predictive performance of the proposed method.