Biases in Maximum Simulated Likelihood Estimation of Bivariate Models

This paper finds that the maximum simulated likelihood (MSL) estimator produces substantial biases when applied to the bivariate normal distribution. A specification of the random parameter bivariate normal model is considered, in which a direct comparison between the MSL and maximum likelihood (ML) estimators is feasible. The analysis shows that MSL produces biased results for the correlation parameter. This paper also finds that the MSL estimator is biased for the bivariate Poisson-lognormal model, developed by Munkin and Trivedi (1999. “Simulated Maximum Likelihood Estimation of Multivariate Mixed-Poisson Regression Models, with Application.” The Econometrics Journal 2: 29–48). A simulation study is conducted, which shows that MSL leads to serious inferential biases, especially large when variance parameters in the true data generating process are small. The MSL estimator produces biases in the estimated marginal effects, conditional means and probabilities of count outcomes.

Analysis of size-grouped potato yield data using a bivariate normal distribution of tuber size and weight

SUMMARYA bivariate normal model is proposed for the joint distribution of potato tuber size and weight. Parameters in the model are estimated from the yields and numbers of tubers in a range of riddle-size categories. The method is illustrated using data from a field experiment; parameters are estimated for each plot, and subjected to analysis of variance. The result is a more succinct summary of treatment effects than that produced in the traditional analysis, where data from each riddle size are analysed separately.

A Bivariate Normal Model of Mechanism Coupler-Point Position

A bivariate normal model of the coupler-point position of a four-bar linkage is presented. Elliptical confidence regions are established as a function of the statistical properties of the mechanism component dimensions. A measure of mechanism merit based on the probability of deviation from mean path is developed. The probabilistic models are verified by Monte Carlo techniques.