title: Music Education in New Zealand Society: Exploring a Meaningful Education

authors: Browne, Jade

subjects: music

abstract: Music has been embedded in cultures throughout history, becoming integral to everyday life. During the last century, scientists have discovered an astonishing link between musical exposure and neurological function. Scientific studies demonstrate that listening to and performing music engages nearly every area of the brain, improving cognitive function, memory and general well-being, suggesting neurological, social and psychological benefits. Despite these discoveries, research indicates that the role of music within New Zealand’s education system has stagnated, being underfunded and undervalued by successive governments. Music is now often perceived as an extracurricular activity, and meaningful music education has become a luxury activity for those who can afford it.

This thesis will outline an account of the role of music in ancient and contemporary cultures, providing historical proof of music’s pre-eminence in the thinking, philosophy and educational activities of civilisations. The benefits of a meaningful musical education will be explored through a comprehensive literature review based on scientific and statistical research. Governmental and public attitudes towards music will also be explored, in order to question the role and value of music education in New Zealand and more broadly in Western society.

text: Music Education in New Zealand Society: Exploring a Meaningful Education Music has been embedded in cultures throughout history, becoming integral to everyday life. During the last century, scientists have discovered an astonishing link between musical exposure and neurological function. Scientific studies demonstrate that listening to and performing music engages nearly every area of the brain, improving cognitive function, memory and general well-being, suggesting neurological, social and psychological benefits. Despite these discoveries, research indicates that the role of music within New Zealand’s education system has stagnated, being underfunded and undervalued by successive governments. Music is now often perceived as an extracurricular activity, and meaningful music education has become a luxury activity for those who can afford it.

This thesis will outline an account of the role of music in ancient and contemporary cultures, providing historical proof of music’s pre-eminence in the thinking, philosophy and educational activities of civilisations. The benefits of a meaningful musical education will be explored through a comprehensive literature review based on scientific and statistical research. Governmental and public attitudes towards music will also be explored, in order to question the role and value of music education in New Zealand and more broadly in Western society.

year: 2017

title: Evaluation of estimators for ill-posed statistical problems subject to multicollinearity

authors: Holland, Luke Murray

subjects: Multicollinearity

abstract: Multicollinearity is a significant problem in economic analysis and occurs in any situation where at least two of the explanatory variables in a model are related to one another. The presence of multicollinearity is problematic, as changes in the dependent variable cannot be accurately attributed to individual explanatory variables. It can cause estimated coefficients to be unstable and have high variances, and thus be potentially inaccurate and inappropriate to guide management or policy. Due to this problem, many alternative estimators have been developed for the analysis of multicollinear data. 
The primary objective of this thesis is to compare and contrast the performance of some of these common estimators, as well as a number of new estimators, and test their prediction accuracy and precision under various circumstances. Through the use of non-trivial Monte Carlo experiments, the estimators are tested under 10 different levels of multicollinearity, with regressors and errors drawn from different distributions (normal,  student t, chi-squared, and in the case of errors, mixed Gaussian). Insights are gained through response surface analysis, which is conducted to help summarise the output of these simulations.
A number of key findings are identified. The highest levels of mean square error (MSE) are generally given by a Generalised Maximum Entropy estimator with narrow support bounds defined for its coefficients (GMEN) and the One-Step Data Driven Entropy (DDE1) model. Yet, none of the estimators evaluated produced sufficiently high levels of MSE to suggest that they were inappropriate for prediction. The most accurate predictions, regardless of the distributions tested or multicollinearity, were given by Ordinary Least Squares (OLS). The Leuven-2 estimator appeared relatively robust in terms of MSE, being reasonably invariant to changes in condition number, and error distribution. However, it was unstable due to variability in error estimation arising from the arbitrary way that probabilities are converted to coefficient values in this framework. In comparison, MSE values for Leuven-1 were low and far more stable than those reported for Leuven-2.
The estimators that produced the least precision risk, as measured through mean square error loss (MSEL), were the GMEN and Leuven-1 estimators. However, the GMEN model requires exogenous information and, as such, is much more problematic to accurately apply in different contexts. In contrast, two models had very poor precision in the presence of multicollinear data, the Two-Step Data Driven Entropy (DDE2) model and OLS, rendering them inappropriate for estimation in such circumstances.
Overall, these results highlight that the Leuven-1 estimator is the most appropriate if a practitioner wishes to achieve high prediction accuracy and precision in the presence of multicollinearity. Nevertheless, it is critical that more attention is paid to the theoretical basis of the Leuven-1 estimator, as relating estimated probabilities to coefficients using concepts drawn from the theory of light appears highly subjective. This is illustrated through the differences in empirical results obtained for the Leuven-1 and Leuven-2 estimators.

text: Evaluation of estimators for ill-posed statistical problems subject to multicollinearity Multicollinearity is a significant problem in economic analysis and occurs in any situation where at least two of the explanatory variables in a model are related to one another. The presence of multicollinearity is problematic, as changes in the dependent variable cannot be accurately attributed to individual explanatory variables. It can cause estimated coefficients to be unstable and have high variances, and thus be potentially inaccurate and inappropriate to guide management or policy. Due to this problem, many alternative estimators have been developed for the analysis of multicollinear data. 
The primary objective of this thesis is to compare and contrast the performance of some of these common estimators, as well as a number of new estimators, and test their prediction accuracy and precision under various circumstances. Through the use of non-trivial Monte Carlo experiments, the estimators are tested under 10 different levels of multicollinearity, with regressors and errors drawn from different distributions (normal,  student t, chi-squared, and in the case of errors, mixed Gaussian). Insights are gained through response surface analysis, which is conducted to help summarise the output of these simulations.
A number of key findings are identified. The highest levels of mean square error (MSE) are generally given by a Generalised Maximum Entropy estimator with narrow support bounds defined for its coefficients (GMEN) and the One-Step Data Driven Entropy (DDE1) model. Yet, none of the estimators evaluated produced sufficiently high levels of MSE to suggest that they were inappropriate for prediction. The most accurate predictions, regardless of the distributions tested or multicollinearity, were given by Ordinary Least Squares (OLS). The Leuven-2 estimator appeared relatively robust in terms of MSE, being reasonably invariant to changes in condition number, and error distribution. However, it was unstable due to variability in error estimation arising from the arbitrary way that probabilities are converted to coefficient values in this framework. In comparison, MSE values for Leuven-1 were low and far more stable than those reported for Leuven-2.
The estimators that produced the least precision risk, as measured through mean square error loss (MSEL), were the GMEN and Leuven-1 estimators. However, the GMEN model requires exogenous information and, as such, is much more problematic to accurately apply in different contexts. In contrast, two models had very poor precision in the presence of multicollinear data, the Two-Step Data Driven Entropy (DDE2) model and OLS, rendering them inappropriate for estimation in such circumstances.
Overall, these results highlight that the Leuven-1 estimator is the most appropriate if a practitioner wishes to achieve high prediction accuracy and precision in the presence of multicollinearity. Nevertheless, it is critical that more attention is paid to the theoretical basis of the Leuven-1 estimator, as relating estimated probabilities to coefficients using concepts drawn from the theory of light appears highly subjective. This is illustrated through the differences in empirical results obtained for the Leuven-1 and Leuven-2 estimators.

year: 2014

title: Te Whakatōhea Maurua

authors: Maxwell, Te Kahautu

abstract: Te Whakatōhea Maurua is a Whakaeke item that was composed to commemorate the rangatira of Te Whakatōhea that lost their lives in the colonial wars of the mid nineteenth century at the hands of the Te Arawa people who were loyalists to the Crown. This composition was composed also to bury the hatchet between Te Whakatōhea and Te Arawa. This composition was performed by Ōpōtiki Mai Tawhiti at the Te Matatini World Championship Kapa Haka Competition 2013

text: Te Whakatōhea Maurua Te Whakatōhea Maurua is a Whakaeke item that was composed to commemorate the rangatira of Te Whakatōhea that lost their lives in the colonial wars of the mid nineteenth century at the hands of the Te Arawa people who were loyalists to the Crown. This composition was composed also to bury the hatchet between Te Whakatōhea and Te Arawa. This composition was performed by Ōpōtiki Mai Tawhiti at the Te Matatini World Championship Kapa Haka Competition 2013

year: 2013