title: A stochastic restricted principal components regression estimator in the linear model.
abstract: We propose a new estimator to combat the multicollinearity in the linear model when there are stochastic linear restrictions on the regression coefficients. The new estimator is constructed by combining the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator, which is called the stochastic restricted principal components (SRPC) regression estimator. Necessary and sufficient conditions for the superiority of the SRPC estimator over the OME and the PCR estimator are derived in the sense of the mean squared error matrix criterion. Finally, we give a numerical example and a Monte Carlo study to illustrate the performance of the proposed estimator.
authors.affiliation: Department of Statistics, Anhui Normal University, Wuhu 241000, China.
authors.forename: Daojiang
authors.identifier: 0000-0002-1152-4980
authors.initials: D
authors.lastname: He
authors.affiliation: Department of Statistics, Anhui Normal University, Wuhu 241000, China.
authors.forename: Yan
authors.identifier: 0000-0001-5213-8560
authors.initials: Y
authors.lastname: Wu
mesh_terms: D008962:Models, Theoretical; D013269:Stochastic Processes