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: Water laws and the cultural values associated with rivers: Current frameworks and future directions.

authors: Campbell, Samuel

subjects: rivers

abstract: The world’s rivers are in ecological decline. They are the most threatened of all freshwater habitats, and threats to their ecological integrity are both increasing and compounding. Rivers are crucial for supporting biological diversity (being unusually biodiverse habitats) and are key to the function of the Earth system. Rivers are also critical for supporting people. They provide food, water for drinking and irrigation, and a significant proportion of the world’s energy. Additionally, people value rivers for their heritage, and the opportunities they provide for aesthetic appreciation and recreation. Rivers also form key components of cosmologies and spiritual practices, and indigenous ways of living and being. These ‘cultural’ values associated with rivers are the focus of this study.

Laws which govern the use and conservation of rivers are generally concerned with safeguarding the socio-economic benefits generated by their utilization. Heritage, aesthetic and recreation interests are recognized to a lesser extent. Each of these provides their own justifications for and approaches to the ecological conservation of rivers. However, the potential role of cultural values (spiritual and indigenous values) in improving ecological outcomes for rivers is underexplored. In this study, I examine the recognition of cultural values associated with rivers in water laws at the international, regional and domestic levels. I ask the question: would greater recognition and implementation of cultural values in water laws improve ecological outcomes for rivers?

I find that the cultural values associated with rivers are heterogeneous and highly context-specific. Their capacity to enhance ecological conservation of rivers is variable. However, some cultural values show real promise in their ability to improve ecological outcomes. I argue that these values should be recognized and implemented in water laws at the domestic, regional and international levels.

text: Water laws and the cultural values associated with rivers: Current frameworks and future directions. The world’s rivers are in ecological decline. They are the most threatened of all freshwater habitats, and threats to their ecological integrity are both increasing and compounding. Rivers are crucial for supporting biological diversity (being unusually biodiverse habitats) and are key to the function of the Earth system. Rivers are also critical for supporting people. They provide food, water for drinking and irrigation, and a significant proportion of the world’s energy. Additionally, people value rivers for their heritage, and the opportunities they provide for aesthetic appreciation and recreation. Rivers also form key components of cosmologies and spiritual practices, and indigenous ways of living and being. These ‘cultural’ values associated with rivers are the focus of this study.

Laws which govern the use and conservation of rivers are generally concerned with safeguarding the socio-economic benefits generated by their utilization. Heritage, aesthetic and recreation interests are recognized to a lesser extent. Each of these provides their own justifications for and approaches to the ecological conservation of rivers. However, the potential role of cultural values (spiritual and indigenous values) in improving ecological outcomes for rivers is underexplored. In this study, I examine the recognition of cultural values associated with rivers in water laws at the international, regional and domestic levels. I ask the question: would greater recognition and implementation of cultural values in water laws improve ecological outcomes for rivers?

I find that the cultural values associated with rivers are heterogeneous and highly context-specific. Their capacity to enhance ecological conservation of rivers is variable. However, some cultural values show real promise in their ability to improve ecological outcomes. I argue that these values should be recognized and implemented in water laws at the domestic, regional and international levels.

year: 2022

title: Kia whakatōmuri te haere whakamua – A Māori framework for coastal climate change adaptation

authors: Bailey-Winiata, Akuhata

subjects: Climate Change Adaptation

abstract: Current climate change adaptation frameworks do not sufficiently represent or acknowledge the intricacies and complex nature of climate adaptation for all communities. This thesis contributes a Māori (Indigenous peoples of Aotearoa New Zealand (A-NZ)) climate adaptation framework that is informed by Te Ao Māori world views, mātauranga Māori (Māori knowledge), Te Tiriti o Waitangi (Treaty of Waitangi) and research at the interface of Western knowledge and mātauranga Māori. This is needed to promote a more equitable and culturally sensitive approach to the current climate change adaptation process for hapū (sub-tribes) and iwi (tribes). To achieve this, this thesis is rooted in the whakataukī (proverb) “Kia whakatōmuri te haere whakamua – I walk backwards into the future with my eyes fixed on my past”, which exemplifies the power of acknowledging Māori history and intergenerational knowledge, while moving forward to a prosperous future. This thesis had four key aims. First, I looked to the past to understand ways Māori ancestors adapted and relocated in response to natural hazards to inform a future climate adaptation or relocation process. Second, I took stock of the contemporary risk to coastal marae (Māori meeting grounds) from sea level rise. Third, I looked internationally at other Indigenous communities' adaptation challenges and how they have overcome them as a mutual learning opportunity. And finally, I developed a conceptual Māori climate adaptation framework based on existing models and informed by a wānanga (workshop) with over 100 Māori participants. This two-part framework emphasises the importance of fostering Te Tiriti-centric relationships and partnerships that are essential for climate adaptation with hapū and iwi. In addition, it serves as a guide to support adaptation decision-making for hapū and iwi Māori. This thesis took a multidisciplinary approach to achieve these aims, incorporating historical and archival analyses, semi-structured interviews, a systematic review, coastal flooding and exposure analyses using spatial information, and wānanga. The findings highlighted that relocation due to natural hazards is not uncommon for Māori, as this thesis identified 51 examples of where relocation was completed or discussed in response to natural hazards. Furthermore, in a case study with Tūhourangi and Ngāti Rangitihi, this thesis identified vital aspects that enabled their relocation following the 1886 Tarawera eruption, the most influential being tuku whenua – the gifting of land to relocate to. This thesis also identified that by 2150, under shared socio-economic pathway (SSP) 5-8.5, 27% and 28% of coastal marae (total of 186 nationally) are exposed to a 100–year and 1000–year annual recurrence interval (ARI) extreme sea level events, respectively. Overall, this thesis contributes to our understanding of the requirements to support hapū and iwi Māori in climate adaptation, with parallels to other Indigenous communities. Requirements include resourcing, partnerships, autonomy, intergenerational planning, recognition, respect and redress. In Chapter 8 – the discussion of this thesis, we focus on four overall contributions this thesis has made, which are: 1) Hapū and iwi Māori are at risk of climate change, 2) We’ve done it before we can do it again, 3) Adaptation approach cannot be one-size-fits-all, and 4) Adaptation in Aotearoa needs a Te Tiriti-centric approach. Ultimately, this thesis underscores the urgent need for inclusive climate adaptation strategies that honour Indigenous knowledge systems, ensuring that hapū and iwi Māori are not only heard but are actively supported in navigating the impacts of climate change.

text: Kia whakatōmuri te haere whakamua – A Māori framework for coastal climate change adaptation Current climate change adaptation frameworks do not sufficiently represent or acknowledge the intricacies and complex nature of climate adaptation for all communities. This thesis contributes a Māori (Indigenous peoples of Aotearoa New Zealand (A-NZ)) climate adaptation framework that is informed by Te Ao Māori world views, mātauranga Māori (Māori knowledge), Te Tiriti o Waitangi (Treaty of Waitangi) and research at the interface of Western knowledge and mātauranga Māori. This is needed to promote a more equitable and culturally sensitive approach to the current climate change adaptation process for hapū (sub-tribes) and iwi (tribes). To achieve this, this thesis is rooted in the whakataukī (proverb) “Kia whakatōmuri te haere whakamua – I walk backwards into the future with my eyes fixed on my past”, which exemplifies the power of acknowledging Māori history and intergenerational knowledge, while moving forward to a prosperous future. This thesis had four key aims. First, I looked to the past to understand ways Māori ancestors adapted and relocated in response to natural hazards to inform a future climate adaptation or relocation process. Second, I took stock of the contemporary risk to coastal marae (Māori meeting grounds) from sea level rise. Third, I looked internationally at other Indigenous communities' adaptation challenges and how they have overcome them as a mutual learning opportunity. And finally, I developed a conceptual Māori climate adaptation framework based on existing models and informed by a wānanga (workshop) with over 100 Māori participants. This two-part framework emphasises the importance of fostering Te Tiriti-centric relationships and partnerships that are essential for climate adaptation with hapū and iwi. In addition, it serves as a guide to support adaptation decision-making for hapū and iwi Māori. This thesis took a multidisciplinary approach to achieve these aims, incorporating historical and archival analyses, semi-structured interviews, a systematic review, coastal flooding and exposure analyses using spatial information, and wānanga. The findings highlighted that relocation due to natural hazards is not uncommon for Māori, as this thesis identified 51 examples of where relocation was completed or discussed in response to natural hazards. Furthermore, in a case study with Tūhourangi and Ngāti Rangitihi, this thesis identified vital aspects that enabled their relocation following the 1886 Tarawera eruption, the most influential being tuku whenua – the gifting of land to relocate to. This thesis also identified that by 2150, under shared socio-economic pathway (SSP) 5-8.5, 27% and 28% of coastal marae (total of 186 nationally) are exposed to a 100–year and 1000–year annual recurrence interval (ARI) extreme sea level events, respectively. Overall, this thesis contributes to our understanding of the requirements to support hapū and iwi Māori in climate adaptation, with parallels to other Indigenous communities. Requirements include resourcing, partnerships, autonomy, intergenerational planning, recognition, respect and redress. In Chapter 8 – the discussion of this thesis, we focus on four overall contributions this thesis has made, which are: 1) Hapū and iwi Māori are at risk of climate change, 2) We’ve done it before we can do it again, 3) Adaptation approach cannot be one-size-fits-all, and 4) Adaptation in Aotearoa needs a Te Tiriti-centric approach. Ultimately, this thesis underscores the urgent need for inclusive climate adaptation strategies that honour Indigenous knowledge systems, ensuring that hapū and iwi Māori are not only heard but are actively supported in navigating the impacts of climate change.

year: 2024-05-28