Inference for the Evolution in Series of Studies

Abstract

Studies will be matrix triplets (X,Dp,Dn), where the matrix X has a row per object and a column per variable, while Dp and Dn are weight matrices for objects and variables, respectively. Given a series of studies (Xi,Dp,Dn),i=1,...,k, we condense the matrix triplets into the Ai = XiDpXtiDn, and use spectral analysis of matrix S = [Sij],i,j = 1,...,k, with Sij = tr(AiAjt) to study the series evolution. When we have a series of studies for each treatment of a basis design we carry out an ANOVA-like inference to study the action of the factors in the base design on the evolution of the series associated to the differents treatments.