Monte Carlo Simulation Comparing Maximum Likelihood and L2 Estimates for ACTH Levels in Equids (Horses)

In Clarke et al (2017) the robustness and efficiency of L2 minimum distance estimators in comparison to maximum likelihood estimators was established for mixtures of normal distributions when the component distributions were not well separated. In a recent investigation of ACTH levels in horses Durham, Clarke, Potier and Hammarstrand (2019) have followed up on Copas and Durham (2012) to show that L2 methods can be used to fit mixture models to the data from a large UK Data Base, obviating the need to carry out expensive experiments on horses. In the process of mixture model fitting we identify “sick” versus “healthy” horses, sick horses having raised levels of ACTH. Since the level of ACTH varies naturally with season, we have identified the estimated mixture distributions for 52 weeks in the year. The purpose of this project is to simulate using Monte Carlo methods the comparison between the maximum likelihood estimator (through use of the EM algorithm) and the L2 method for parameter values in the range of values that are arrived at for these data. This may reinforce the argument that L2 methods should be used for these analyses. The candidate will need to use already written routines written in R to do the comparisons and produce and interpret summary comparisons.

George Malone

Murdoch University

George Malone is a third-year student at Murdoch University, studying a Bachelor’s degree majoring in Mathematics & Statistics. He has previously been employed by Murdoch University as a Peer Assisted Study Leader and Peer Academic Coach, and by Curtin University as a Research Assistant at the Centre for Crop and Disease Management. He is currently employed by the Centre for Comparative Genomics at Murdoch University as a Research Assistant, providing quality assurance testing and documentation for the Rare Disease Registry Framework. His main area of interest in his field of study was originally applied mathematics, but recently he has been enjoying learning applications of statistical methods. He retains an interest in calculus, but his focus is now on statistics, with a particular interest in biostatistics.

After growing up in a rural area, coming from a family with strong agricultural roots, his interest in and exposure to botanical and zoological studies has eventually led him to engage in projects in biostatistics. He completed a summer research project in the School of Engineering and Information Technology at Murdoch University last year for Associate Professor Nicola Armstrong and Dr Claire Sharp, relating to factors affecting survival in canine veterinary trauma subjects. The AMSI Vacation Research Scholarship in which he has been engaged, for Dr Brenton Clarke, relates to assessing the applicability of robust parametric methods in the estimation of adrenocorticotropic hormone levels in jumentous samples, in an attempt to provide an alternative method for assessing the health of equine subjects to invasive and expensive procedures.

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