Showing papers by "T. W. Anderson published in 1978"

Repeated Measurements on Autoregressive Processes

Abstract: Estimation of parameters and tests of hypotheses are studied in first-order autoregressive processes where the process is observed several times over a given time interval. The process may be homogeneous (i.e., the parameters may be constant over time) or inhomogeneous (time-varying parameters). Sufficient statistics under normality are obtained for various cases and several tests of hypotheses are given.

Maximum Likelihood Estimation for Vector Autoregressive Moving Average Models

Abstract: : The vector autoregressive moving average model is a multivariate stationary stochastic process where the unobservable multivariate process consists of independently identically distributed random vectors. The coefficient matrices and the covariance matrix are to be estimated from an observed sequence. Under the assumption of normality the method of maximum likelihood is applied to likelihoods suitably modified for techniques in the frequency and time domains. Newton-Raphson and scoring iterative methods are presented.

An extremal problem for positive definite matrices

Abstract: : A problem studied by Flanders is to minimize the function f(R) = tr (SR + T 1/R) over the set of positive definite matrices R, where S and T are positive semi-definite matrices of rank m. Alternative proofs that may have some intrinsic interest are provided. The proofs explicitly yield the infimum to f(R) . One proof is based on a convexity argument and the other on a sequence of reductions to a univariate problem.