title: A new approach to fitting linear models in high dimensional spaces

authors: Wang, Yong

abstract: This thesis presents a new approach to fitting linear models, called “pace regression”, which also overcomes the dimensionality determination problem. Its optimality in minimizing the expected prediction loss is theoretically established, when the number of free parameters is infinitely large. In this sense, pace regression outperforms existing procedures for fitting linear models. Dimensionality determination, a special case of fitting linear models, turns out to be a natural by-product. A range of simulation studies are conducted; the results support the theoretical analysis. 

Through the thesis, a deeper understanding is gained of the problem of fitting linear models. Many key issues are discussed. Existing procedures, namely OLS, AIC, BIC, RIC, CIC, CV(d), BS(m), RIDGE, NN-GAROTTE and LASSO, are reviewed and compared, both theoretically and empirically, with the new methods. 

Estimating a mixing distribution is an indispensable part of pace regression. A measure-based minimum distance approach, including probability measures and nonnegative measures, is proposed, and strongly consistent estimators are produced. Of all minimum distance methods for estimating a mixing distribution, only the nonnegative-measure-based one solves the minority cluster problem, what is vital for pace regression.

Pace regression has striking advantages over existing techniques for fitting linear models. It also has more general implications for empirical modeling, which are discussed in the thesis.

text: A new approach to fitting linear models in high dimensional spaces This thesis presents a new approach to fitting linear models, called “pace regression”, which also overcomes the dimensionality determination problem. Its optimality in minimizing the expected prediction loss is theoretically established, when the number of free parameters is infinitely large. In this sense, pace regression outperforms existing procedures for fitting linear models. Dimensionality determination, a special case of fitting linear models, turns out to be a natural by-product. A range of simulation studies are conducted; the results support the theoretical analysis. 

Through the thesis, a deeper understanding is gained of the problem of fitting linear models. Many key issues are discussed. Existing procedures, namely OLS, AIC, BIC, RIC, CIC, CV(d), BS(m), RIDGE, NN-GAROTTE and LASSO, are reviewed and compared, both theoretically and empirically, with the new methods. 

Estimating a mixing distribution is an indispensable part of pace regression. A measure-based minimum distance approach, including probability measures and nonnegative measures, is proposed, and strongly consistent estimators are produced. Of all minimum distance methods for estimating a mixing distribution, only the nonnegative-measure-based one solves the minority cluster problem, what is vital for pace regression.

Pace regression has striking advantages over existing techniques for fitting linear models. It also has more general implications for empirical modeling, which are discussed in the thesis.

year: 2000

title: Seeing is believing: telling the ‘inside’ story of a beginning masters athlete through film

authors: Kluge, Mary Ann

subjects: visual research methods

abstract: This paper is about how a previously inactive woman with little or no experience of playing sports became a masters athlete at 65 years of age. The authors explore how visual methods as a different way of knowing can be used to enhance our current theories and practical knowledge about older adults' experiences with sport and exercise. How data were gathered and analysed through film and how film was used to represent experience are described. Additionally, the authors offer their perspective on some challenges and/or ethical issues researchers may face when visual methods are used.

text: Seeing is believing: telling the ‘inside’ story of a beginning masters athlete through film This paper is about how a previously inactive woman with little or no experience of playing sports became a masters athlete at 65 years of age. The authors explore how visual methods as a different way of knowing can be used to enhance our current theories and practical knowledge about older adults' experiences with sport and exercise. How data were gathered and analysed through film and how film was used to represent experience are described. Additionally, the authors offer their perspective on some challenges and/or ethical issues researchers may face when visual methods are used.

year: 2010-07

title: He Piko, He Repo: Environmental DNA as a biomonitoring tool for wetland restoration

authors: Bird, Starsha

subjects: colonisation

abstract: Wetlands are biodiversity hotspots, harbouring distinctive species while providing numerous ecosystem services. Unfortunately, throughout human civilisation, they have been systematically degraded, resulting in a dramatic global loss in wetland extent, the establishment of invasive species and the extinction of many natives and, in Aotearoa New Zealand, impediment of the special connection Māori share with their repo (wetlands). Monitoring wetland biodiversity to take appropriate restorative action and minimise further degradation is imperative, particularly in the face of climate change. Environmental DNA (eDNA; genetic material released by organisms into the environment) is an increasingly popular non-invasive biomonitoring method that provides information about the presence or potential absence of species inhabiting a given ecosystem, but has yet to be optimised for wetland environments. My thesis aimed to address the consequences of colonisation on the relationship between Māori and their wetlands, and to explore the value eDNA holds for wetland biomonitoring. The first analysis (Chapter 2) delved into the past (post-European settlement; 1840s), the present (2023), and the future (2073) of Opuatia Wetland (Waikato, Aotearoa New Zealand) through a series of interviews with three individuals who whakapapa to (are connected with) Opuatia Wetland and its surroundings. I found that Opuatia Wetland once flourished with native biodiversity, and kai (food) was readily available. However, land confiscation by European settlers marked the downfall of this once productive and connected catchment such that it is presently in a fairly degraded state, dominated by exotic species, with Māori feeling disconnected from their whenua (land). Considering the future, the interviewees envisioned a revived abundance of native species and desire for restoration efforts to be facilitated by both mātauranga Māori (Māori knowledge) and science. The second analysis (Chapter 3) examined a publicly available eDNA database to retrieve data from 26 wetland sites across Aotearoa New Zealand to understand taxonomic diversity patterns. Here, I showed that DNA sequence composition varied across the motu (country), illustrating that varying environmental conditions among wetland types influences biodiversity. Notably, most sites were dominated by >50% exotic species. These findings highlight the value of publicly shared data for generating new insights, and the need for resource allocations to tackle the persistence of exotic species in wetland ecosystems. The third analysis (Chapter 4) focused on analysing biodiversity dynamics at a single wetland and tested various eDNA sampling techniques. I sampled four spatially distant sites across Opuatia Wetland at three time points during an austral spring and simultaneously obtained data from conventional taxonomic surveys, tested three different filter sizes, and assessed DNA degradation rates using foreign DNA. I found significant differences in biodiversity across time and space, and when using different eDNA collection filters. Foreign DNA persisted for up to one week post-release within a 10 m radius, and combining conventional and eDNA methods provided a more comprehensive overview of biodiversity patterns. These findings collectively showcased key changes in biodiversity, even over short spatial and temporal scales, and identified parameters to consider for wetland biodiversity monitoring and associated data interpretation. It is only a matter of time until the impacts of climate change and invasive species take firmer hold of Aotearoa New Zealand's distinctive and fragile environment. Undoubtedly, eDNA can be part of the solution to mitigate these challenges, owing to its versatility across ecosystem types, capacity to extend to various substrates, and accessibility for researchers and citizen scientists alike. As eDNA methods continue to improve and become integrated into ongoing biomonitoring schemes, building equitable and empowering relationships between Māori and researchers/government bodies will best ensure that Aotearoa New Zealand repo and other environments are maintained and conserved for future generations.

text: He Piko, He Repo: Environmental DNA as a biomonitoring tool for wetland restoration Wetlands are biodiversity hotspots, harbouring distinctive species while providing numerous ecosystem services. Unfortunately, throughout human civilisation, they have been systematically degraded, resulting in a dramatic global loss in wetland extent, the establishment of invasive species and the extinction of many natives and, in Aotearoa New Zealand, impediment of the special connection Māori share with their repo (wetlands). Monitoring wetland biodiversity to take appropriate restorative action and minimise further degradation is imperative, particularly in the face of climate change. Environmental DNA (eDNA; genetic material released by organisms into the environment) is an increasingly popular non-invasive biomonitoring method that provides information about the presence or potential absence of species inhabiting a given ecosystem, but has yet to be optimised for wetland environments. My thesis aimed to address the consequences of colonisation on the relationship between Māori and their wetlands, and to explore the value eDNA holds for wetland biomonitoring. The first analysis (Chapter 2) delved into the past (post-European settlement; 1840s), the present (2023), and the future (2073) of Opuatia Wetland (Waikato, Aotearoa New Zealand) through a series of interviews with three individuals who whakapapa to (are connected with) Opuatia Wetland and its surroundings. I found that Opuatia Wetland once flourished with native biodiversity, and kai (food) was readily available. However, land confiscation by European settlers marked the downfall of this once productive and connected catchment such that it is presently in a fairly degraded state, dominated by exotic species, with Māori feeling disconnected from their whenua (land). Considering the future, the interviewees envisioned a revived abundance of native species and desire for restoration efforts to be facilitated by both mātauranga Māori (Māori knowledge) and science. The second analysis (Chapter 3) examined a publicly available eDNA database to retrieve data from 26 wetland sites across Aotearoa New Zealand to understand taxonomic diversity patterns. Here, I showed that DNA sequence composition varied across the motu (country), illustrating that varying environmental conditions among wetland types influences biodiversity. Notably, most sites were dominated by >50% exotic species. These findings highlight the value of publicly shared data for generating new insights, and the need for resource allocations to tackle the persistence of exotic species in wetland ecosystems. The third analysis (Chapter 4) focused on analysing biodiversity dynamics at a single wetland and tested various eDNA sampling techniques. I sampled four spatially distant sites across Opuatia Wetland at three time points during an austral spring and simultaneously obtained data from conventional taxonomic surveys, tested three different filter sizes, and assessed DNA degradation rates using foreign DNA. I found significant differences in biodiversity across time and space, and when using different eDNA collection filters. Foreign DNA persisted for up to one week post-release within a 10 m radius, and combining conventional and eDNA methods provided a more comprehensive overview of biodiversity patterns. These findings collectively showcased key changes in biodiversity, even over short spatial and temporal scales, and identified parameters to consider for wetland biodiversity monitoring and associated data interpretation. It is only a matter of time until the impacts of climate change and invasive species take firmer hold of Aotearoa New Zealand's distinctive and fragile environment. Undoubtedly, eDNA can be part of the solution to mitigate these challenges, owing to its versatility across ecosystem types, capacity to extend to various substrates, and accessibility for researchers and citizen scientists alike. As eDNA methods continue to improve and become integrated into ongoing biomonitoring schemes, building equitable and empowering relationships between Māori and researchers/government bodies will best ensure that Aotearoa New Zealand repo and other environments are maintained and conserved for future generations.

year: 2023