We analyse the simplest two-equation seemingly unrelated regressions model and demonstrate that its likelihood may have up to five stationary points, and thus there may be up to three local modes. Consequently the estimates obtained via iterative estimation methods may depend on starting values....

In a proportional representation system, apportionment methods are used to round the vote proportion of a party to an integer number of seats in parliament. Assuming uniformly distributed vote proportions, we derive the seat allocation distributions for stationary divisor methods. An important...

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call iterative conditional fitting, for computing the maximum likelihood estimate of the constrained covariance matrix,...

We consider normal [reverse not equivalent] Gaussian seemingly unrelated regressions (SUR) with incomplete data (ID). Imposing a natural minimal set of conditional independence constraints, we find a restricted SUR/ID model whose likelihood function and parameter space factor into the product of...

Apportionment methods round vote proportions to integer numbers of seats in a parliament. The seat excess is the difference between the integer seat allocation and the fractional ideal share of seats. In order to quantify biased treatment of larger versus smaller parties, previous studies...

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses...

When testing geometrically irregular parametric hypotheses, the bootstrap is an intuitively appealing method to circumvent difficult distribution theory. It has been shown, however, that the usual bootstrap is inconsistent in estimating the asymptotic distributions involved in such problems....

The Behrens-Fisher problem concerns testing the equality of the means of two normal populations with possibly different variances. The null hypothesis in this problem yields a statistical model for which the likelihood function may have more than one local maximum. We show that if the null...