Multivariate functional least squares
This paper develops a robust large sample method for estimating the regression coefficient in a multivariate regression model when the elements in the error term have long-tailed and possibly asymmetric marginal distributions. The approach is to extend the so-called method of functional least squares [see the author, J. Appl. Probab., Spec. Vol. 19A, 225-239 (1982; Zbl 0492.62053)] from the univariate case to the multivariate case. 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. The estimation in multivariate autoregressive processes is discussed.
scientific article; zbMATH DE number 4094596
scientific article