A Note on the W Transformation

A matrix transformation, named the W transformation by Hemmerle and Hartley [3], is useful in the maximum likelihood estimation of a mixed analysis of variance model. A simpler computational form for W is suggested.     

A Method of Estimating Variance Components in Unbalanced Designs

Another method of estimating variance components in the unbalanced case is presented for a general model with unbalanced population structure and unequal variances over the population. The method utilizes unweighted means and can be shown to give unbiased estimates when the numbers of observations are sampled and certain to be > 1. When the design is balanced the estimators coincide with the usual anova-estimators. The construction of estimators is exemplified for four situations with factors crossed and nested in different ways.     

Maximum Likelihood Estimation for the Multinomial Distribution Using Geometric Progamming

The problem of obtaining maximum likelihood estimates for the multinomial distribution is considered. Maximum likelihood estimation is applied to the particular problem of estimating overlap sizes created by interlocking sampling frames. In this paper, geometric programming is discusseda as a method of solving the likelihood function and is applied to a practical example of estimating overlap sizes.     

A Numerical Investigation of Several One-Dimensional Search Procedures in Nonlinear Regression Problems

The solution of nonlinear regression problems often requires the use of iterative algorithms in order to obtain the best possible set of parameters. It has become apparent that the inclusion of a one-dimensional search procedure between iterations is generally beneficial for improving both convergence and rates of convergence. There are a number of different search procedures currently in use and this report investigates five of them by using the modified Gauss-Newton iterative algorithm with and without second partial derivatives. Four different measures of effectiveness, related to the accuracy and efficiency of the total algorithm, are used to rate the search procedures. Trials on two nonlinear regression problems of three and six parameters show that although a certain degree of accuracy in the search procedure is necessary, an increase in accuracy does not necessarily improve the performance of the total algorithm.