For a stationary autoregressive process of order p and disturbance variance [sigma]2 it is shown that the determinant of the covariance of T (=p) consecutive random variables of the process is ([sigma]2)T [Pi]i,j=1p (1 - wiwj)-1, where w1, ..., wp are the roots of the associated polynomial...

The likelihoood function of the Gaussian MA(1) zero-mean can be expressed in terms of the variance of the process and the first-order autocorrelation or alternatively in terms of the variance of the unobservable independent normal random variables and the moving average coefficient. The...

In the multivariate one-way classification with fixed or random effects the between-group effects may be restricted to a lower dimensional space. The problem of testing the dimension of the effect space is treated. For the balanced random effect model the asymptotic null distribution of the...

In the balanced multivariate components of variance the likelihood ratio criterion depends on the roots of a determinantal equation involving the "between" and "within" matric sums of squares. The limiting distribution of -2 times the logarithm of the criterion is characterized; it is not a...

The asymptotic distribution of the sample canonical correlations and coefficients of the canonical variates is obtained when the nonzero population canonical correlations are distinct and sampling is from the normal distribution. The asymptotic distributions are also obtained for reduced rank...