Multivariate functional least squares

Abstract

The paper is concerned with estimating multivariate linear and autoregressive models using a generalisation of the functional least-squares procedure. This leads to a family of estimators, indexed by a vector parameter, for which strong uniform consistency and weak convergence results are established. The structure of the limiting covariance matrix is explored and an adaptive estimator with an appropriately "small" covariance matrix is proposed. This estimator is asymptotically normally distributed and it is claimed that its use is particularly appropriate for models with long-tailed and possibly asymmetric error distributions.