Multivariate functional least squares
type: Item
instance of: scholarly article
title: Multivariate functional least squares
zbMATH Open document ID: 0668.62034
DOI: 10.1016/0047-259X(88)90152-2
author: Christopher R. Heathcote
author: Alan H. Welsh
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 4094596
zbMATH Keywords: robust large sample method
zbMATH Keywords: multivariate regression model
zbMATH Keywords: asymmetric marginal distributions
zbMATH Keywords: functional least squares
zbMATH Keywords: strong uniform consistency
zbMATH Keywords: weak convergence
zbMATH Keywords: limiting covariance matrix
zbMATH Keywords: adaptive estimator
zbMATH Keywords: multivariate autoregressive processes
reviewed by: Chien-Pai Han
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4094596