Componentes Principais Estocasticamente Restritos

Abstract

The main scope of this paper is to extend the Restricted Principal Camponent Analysis (ACP-R) firstly proposed by D'Ambra and Lauro (1982) and Amato (1988) to a stochastic framework. After presenting the ACP-R (Section 2), we show how the stochastic restrictions can be inserted into the classical analysis of the General Linear Madel. Theoretical and empirical matrices for stochastically restricted principal components (ACP-RA) are derived for both cases of known and unknown matrix-norm for directed projections of analytical variables on the restriction's subspace. Section 3 present applications of ACP-RA matrices for a particular structure of residual variability, namely, the autoregressive process. In Section 4 the ACP-RA approach is extended to more general structures of residual variability applied in a context of multiple restrictions' subspaces.