Approximate marginal inference in models with stratum nuisance parameters, with applications to fishery data

• Main Author: Tobin, Jared, 1983-
• Other Authors: Memorial University of Newfoundland. Dept. of Mathematics and Statistics
• Format: Thesis
• Language: English
• Published: 2010
• Subjects: Fisheries > Statistics; Estimation theory; Newfoundland studies; University of Newfoundland
• Online Access: http://collections.mun.ca/cdm/ref/collection/theses5/id/18327

Thesis (M.A.S.)--Memorial University of Newfoundland, 2011. Mathematics and Statistics Bibliography: leaves 85-88. The profile likelihood is commonly used in cases where the maximum likelihood estimator for a shape or dispersion parameter depends on knowledge of the mean. We demonstrate that, in stratified models with many mean parameters, the maximum profile likelihood estimator for a common shape parameter can be severely biased or even inconsistent when the sample size per stratum is low. We note a 'marginal' likelihood function that eliminates these problematic mean parameters, but is usually intractable or even impossible to calculate in practice. We discuss approximations to this marginal likelihood - notably the modified profile likelihood of Barndorff-Nielsen [5], the adjusted profile likelihood of Cox & Reid [16], and quasi-likelihood variants - and demonstrate that estimators based on these functions have better bias properties than those based on the full likelihood. We apply these estimators to a stratified negative binomial model and achieve accurate estimates for the negative binomial dispersion parameter k in a simulation experiment. Finally, we provide an application of our methods to fishery data.