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...

We develop the likelihood ratio criterion (LRC) for testing the coefficients of a structural equation in a system of simultaneous equations in econometrics. We relate the likelihood ratio criterion to the AR statistic proposed by Anderson and Rubin (1949, 1950), which has been widely known and...

We consider the estimation of the coefficients of a linear structural equation in a simultaneous equation system when there are many instrumental variables. We derive some asymptotic properties of the limited information maximum likelihood (LIML) estimator when the number of instruments is large;...

We compare four different estimation methods for the coefficients of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the...

We compare four dffierent estimation methods for a coefficient of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the...

When an econometric structural equation includes two endogenous variables and their coefficients are normalized so that their sum of squares is 1, it is natural to express them as the sine and cosine of an angle. The Limited Information Maximum Likelihood (LIML) estimator of this angle when the...

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...