title: Using finite mixtures to robustify statistical models

authors: Rohan, Maheswaran

subjects: Robust Statistics

abstract: This thesis is concerned with robust estimation of the parameters of statistical models. Although robust estimation is a very good idea, it has some shortcomings when seen from the statistical modelling point of view. For example, there are no easily applicable principles for creating robust estimates in new situations. In this thesis, we are trying to introduce a unified method to obtain the robustified statistics for various situations such as the linear model and the generalized linear model. We wish to modify the maximum likelihood estimation procedure, which is very sensitive to the outliers. In order to reduce the effect on these estimates by outliers, we add an additional component, which would be of no interest but would contain all outliers, to the regular component forming a finite mixture. In fact, we use the finite mixture model to obtain a ``robustified'' estimate for a model parameter $\theta$, where the finite mixture form is being used as a mathematical tool to have a tractable form of analysis rather than being used as a serious model for the data. We employ the EM algorithm to obtain the our proposed robustified estimates for the parameters. Our estimates are compared with some other estimates defined in the robust statistics literature. This thesis examines the robustness of the proposed estimates using the concept of influence function. The estimates are defined iteratively, so that the implicit differentiation method of Jorgensen is used to obtain the influence functions of the estimates. We give example plots of these influence functions which are bounded. In this thesis, we give mathematical results for all cases and we use well known real data sets to investigate our method. The statistical software R is used for all investigation. Finally, we hope that this method may give a unified approach for making parameter estimation in statistical models more robust.

text: Using finite mixtures to robustify statistical models This thesis is concerned with robust estimation of the parameters of statistical models. Although robust estimation is a very good idea, it has some shortcomings when seen from the statistical modelling point of view. For example, there are no easily applicable principles for creating robust estimates in new situations. In this thesis, we are trying to introduce a unified method to obtain the robustified statistics for various situations such as the linear model and the generalized linear model. We wish to modify the maximum likelihood estimation procedure, which is very sensitive to the outliers. In order to reduce the effect on these estimates by outliers, we add an additional component, which would be of no interest but would contain all outliers, to the regular component forming a finite mixture. In fact, we use the finite mixture model to obtain a ``robustified'' estimate for a model parameter $\theta$, where the finite mixture form is being used as a mathematical tool to have a tractable form of analysis rather than being used as a serious model for the data. We employ the EM algorithm to obtain the our proposed robustified estimates for the parameters. Our estimates are compared with some other estimates defined in the robust statistics literature. This thesis examines the robustness of the proposed estimates using the concept of influence function. The estimates are defined iteratively, so that the implicit differentiation method of Jorgensen is used to obtain the influence functions of the estimates. We give example plots of these influence functions which are bounded. In this thesis, we give mathematical results for all cases and we use well known real data sets to investigate our method. The statistical software R is used for all investigation. Finally, we hope that this method may give a unified approach for making parameter estimation in statistical models more robust.

year: 2011

title: Discourse on the operationalisation of and accounting for development in a Fijian context

authors: Ali, Nur Bano

abstract: The differentiation of social practices between societies, be it accounting or any other social science discipline, constitutes the foundation and premise upon which this thesis is constructed. With this as the initial motivating factor, and through an analysis and assessment of the Fiji Development Bank (FDB) as a development institution (the only institution committed to development in Fiji by its official charter), the study aspires to give prominence to the need to locate contextually, the workings of institutions such as these. A reflection upon the operationalisation of development in Fiji through the FDB will illuminate the comprehension of this concept, both in Fiji and globally. From this perspective then the omni-present nature of both development and accounting practices will be examined for contextual differences. A contextual analysis which is incorporative of a society’s social, political, economic, and historical circumstances is necessary to understand in depth, its practices and institutions as opposed to some generalised universal application. Such a contextual sensitivity is integral to a critical analysis today and is central to this study. 

Integral to, and in conformity with the concern to differentiate, is the need to problematise the exclusionary nature of accounting practices which are universally applied for the measurement of concepts such as development.

text: Discourse on the operationalisation of and accounting for development in a Fijian context The differentiation of social practices between societies, be it accounting or any other social science discipline, constitutes the foundation and premise upon which this thesis is constructed. With this as the initial motivating factor, and through an analysis and assessment of the Fiji Development Bank (FDB) as a development institution (the only institution committed to development in Fiji by its official charter), the study aspires to give prominence to the need to locate contextually, the workings of institutions such as these. A reflection upon the operationalisation of development in Fiji through the FDB will illuminate the comprehension of this concept, both in Fiji and globally. From this perspective then the omni-present nature of both development and accounting practices will be examined for contextual differences. A contextual analysis which is incorporative of a society’s social, political, economic, and historical circumstances is necessary to understand in depth, its practices and institutions as opposed to some generalised universal application. Such a contextual sensitivity is integral to a critical analysis today and is central to this study. 

Integral to, and in conformity with the concern to differentiate, is the need to problematise the exclusionary nature of accounting practices which are universally applied for the measurement of concepts such as development.

year: 1998

title: Takitoru: creative practice toward the development of a trilingual dramaturgical kaupapa

authors: Lodge, Alexandra Rose Pittaway

subjects: theatre

abstract: I have focused on writing a play in the three languages of Aotearoa: New Zealand Sign Language, te reo Māori, and NZ English. Through the development of this script with three actors I have found techniques for performance and workshopping to encourage multilingual creative practice for a playwright. Through case studies of playwrights doing similar work at an international level, I have synthesised analytical and creative research into a final script and summary of my dramaturgical findings.
Through creative practice in scriptwriting and developmental workshops, this research explores what story-telling modes, devices or styles seem particularly apt for conveying an inclusive and engaging trilingual narrative on stage.
This specifically involves developing a dramaturgical set of insights for others who may want to do cross-language performance in Aotearoa.

text: Takitoru: creative practice toward the development of a trilingual dramaturgical kaupapa I have focused on writing a play in the three languages of Aotearoa: New Zealand Sign Language, te reo Māori, and NZ English. Through the development of this script with three actors I have found techniques for performance and workshopping to encourage multilingual creative practice for a playwright. Through case studies of playwrights doing similar work at an international level, I have synthesised analytical and creative research into a final script and summary of my dramaturgical findings.
Through creative practice in scriptwriting and developmental workshops, this research explores what story-telling modes, devices or styles seem particularly apt for conveying an inclusive and engaging trilingual narrative on stage.
This specifically involves developing a dramaturgical set of insights for others who may want to do cross-language performance in Aotearoa.

year: 2020