Larry M. Pearson

Case-deletion diagnostics for mixed models

Mixed linear models arise in many areas of application. Standard estimation methods for mixed models are sensitive to bizarre observations. Such influential observations can completely distort an analysis and lead to inappropriate actions and conclusions. We develop case-deletion diagnostics for detecting influential observations in mixed linear models. Diagnostics for both fixed effects and variance components are proposed. Computational formulas are given that make the procedures feasible. The methods are illustrated using examples.

Covariance function diagnostics for spatial linear models

Case deletion diagnostics are developed for detecting observations that are influential in estimating the covariance function of a spatial random field. Diagnostics are developed within the context of universal kriging. Computational formulae are given that make the procedures feasible and the diagnostics are illustrated in an example.

Estimation in two-parameter exponential distributions

Exponential distributions are used extensively in the field of life-testing. Estimation of parameters is revisited in two-parameter exponential distributions. A comparison study between the maximum likelihood method, the unbiased estimates which are linear functions of the maximum likelihood method, the method of product spacings, and the method of quantile estimates are presented. Finally, a simulation study is given to demonstrate the small sample properties

Quantiles for finite mixtures of normal distributions

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized.

A note on estimating parameters in two-parameter Pareto distributions

Pareto distributions are used extensively in modelling income distributions. Estimation of parameters is revisited in two-parameter Pareto distributions. The method of quantile estimates using the elemental estimates and the method of product spacings are applied to the two-parameter Pareto distributions. A comparative study between the maximum likelihood method, the unbiased estimates which are functions of the maximum likelihood method, the minimum mean squared error method, the method of moments, the method of quantile estimation, the method of quantile estimation using the elemental estimates and the method of product spacings is presented.

A Monte Carlo comparison of Bayesian estimators and trimmed means

We indicate the usefulness of a Bayesian method of estimating a mean in the face of mean shift contamination (symmetric and asymmetric). We provide simple approximate Bayesian confidence interval formulas, and make appropriate comparisons, via Monte Carlo study, with procedures based on trimmed means, Tiku’s MML estimates, and the sample mean. We also indicate the global power of test procedures based on these estimators.