A matrix algebraic method of order selection is proposed for ARMA time series modeling for situations in which both inputs and outputs are observed in additive noise with known variances. Such situations include observational studies in which all observations-those of both inputs and outputs-are erred and controlled experiments in which outputs are observed with error while inputs are observed without error. The proposed method is based on the eigenvalue structure of the covariance matrices associated with the observed data and performs well for short data records at moderate SNRs.

A detector of a spatially distributed target in white Gaussian noise is developed. A reasonable distribution for the a priori target scatterer density is assumed, and a detector that incorporates this a priori knowledge is given. A simple detector form results, whose detection performance is robust over different scattering densities.

A sharp upper bound on the probability of false alarm, P/sub F/, of a matched filter bank detector over the class of input variates that are zero mean and have a specified covariance matrix, R/sub xx/, is derived. This bound is a function of the detector threshold, T, and R/sub xx/. It is shown that the bound is inversely proportional to T/sup 2/. Hence there may be a wide variation of P/sub F/ over the class since the P/sub F/ for Gaussian inputs varies as exp(-T/sup 2/).>

A robust locally optimum detector of a signal embedded in additive dependent nonGaussian noise is presented. The performance criterion is Bayes risk, the sample size is finite, and the uncertainty class of multivariate inputs is the in -contamination model. The locally optimum detector is shown to be a censored version of the nominal likelihood ratio.>