Theoretical framework for local PLS1 regression, and application to a rainfall data set

A new multivariate non-parametric regression method is considered, which is an extension of PLS1 regression using the multivariate local polynomial regression framework. A theoretical framework that can be used in order to study the asymptotic properties of the estimator is proposed, and the method is implemented on a real data set, made up of seasonal amounts of rainfall in the north of the Nordeste region of Brazil, to be explained by climatic variables. The performances of the three methods of PLS1 regression, multivariate local regression and local PLS1 regression are compared by means of cross-validation and the use of a validation period. All calculations have been implemented in the S-Plus package. The results confirm the good properties of local PLS1 regression.