Estimation of common linear functional relationships in k data sets

This paper studies a functional-type linear measurement-error model, in which k data sets of observations are assumed to have in common a set of linear restrictions on their respective unobservable constant vectors. Each data set consists of replicated measurements of each one of several, generally unequal, constant vectors, with normal error assumed independent for each measurement made. The error covariance matrices are unspecified, and are equal for measurements within a data set but in general unequal among the data sets. This work generalises the results of Anderson (1951, 1984), who derived maximum likelihood estimators for the constant vectors and error covariance matrix of a single such data set. The model recalls the common-space analysis described by Flury (1987; 1988, pp. 131-4), but differs by the presence of a fixed effects subspace. Maximum likelihood estimation of the model parameters requires special numerical methods. An example from electroencephalography is;used to introduce and illustrate the method.