PARTIAL LEAST SQUARES REGRESSION $PLS$ ON INTERVAL DATA

Uncertainty in the data can be considered as a numerical interval in which a variable can assume its possible values, this has been known as interval data. In this paper the $PLS$ regression methodology is extended to the case where explanatory, response variables and coefficients regression are intervals. In this way a regression methodology solves three problems encountered with actual data type is proposed: first multicollinearity in explanatory and response variables, second real data does not belong to a Euclidean space and finally, problems when uncertainty in the data is represented by intervals. Today there are common tasks, such as planning and operation of electrical systems, production planning, transport logistics, inventory, management of securities portfolios; among others, involving uncertainty; this way models that take into account and the ability to make decisions for optimal results from a range of possibilities or scenarios are required. Furthermore, the analysis of real data is affected by different types of errors as measurement errors, miscalculations and imprecision related to the method adopted for estimating data. This paper is a methodological proposal of theoretical type and is based on development about mathematical optimization on multi-interval and multi-matrix spaces.