A statistical analysis of water quality data collected on paired agricultural watersheds was undertaken. The objective of the study was to evaluate trends in water quality. The data sets that were used to determine the changes in water quality were taken from the project "Gestion de leau dans le bassin versant de la partie superieure du ruisseau St. Esprit". For the period from 1994 to 1996, the analysed water quality parameter were nitrate, phosphate, ammonium, potassium, total Kjeldahl nitrogen, total phosphorus and suspended sediment. / The data sets were analysed using descriptive statistics, graphical techniques and non-parametric methods to detect trends in the measured water quality parameters. The statistical analyses were undertaken to determine the effects of soil conservation practices and fertiliser management and to compare different sampling strategies. / The analyses showed that there were no detectable changes in water quality over the 3-year period related to the conservation practices. The lack of improvement in water quality might be due to the slow rate of adoption of conservation practices and to climatic variations. / For the non-parametric methods applied, it was possible to show that climatic variations on small watershed affect the results over a short time period (<5 years). The phosphate concentration on the control showed a significant upward trend. The nitrate concentration on St. Esprit showed an upward trend over the 3-year period and then downward trend after a 4-year period of water quality data. This was likely due to the implementation of best management practices. / The statistical analyses showed that weekly sampling on fixed schedule produce the same results as automated sampling based upon flow rate related to a defined discharge. This shows that the more complex and expensive flow weighted sampling scheme is not required to detect trends in water quality.

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This thesis focuses on construction, properties and estimation of asymmetric heavy-tailed distributions, as well as on their applications to financial modeling and risk measurement. First of all, we suggest a general procedure to construct a fully asymmetric distribution based on a symmetrically parametric distribution, and establish some natural relationships between the symmetric and asymmetric distributions. Then, three new classes of asymmetric distributions are proposed by using the procedure: the Asymmetric Exponential Power Distributions (AEPD), the Asymmetric Student-t Distributions (ASTD) and the Asymmetric Generalized t Distribution (AGTD). For the first two distributions, we give an interpretation of their parameters and explore basic properties of them, including moments, expected shortfall, characterization by the maximum entropy property, and the stochastic representation. Although neither distribution satisfies the regularity conditions under which the ML estimators have the usual asymptotics, due to a non-differentiable likelihood function, we nonetheless establish asymptotics for the full MLE of the parameters. A closed-form expression for the Fisher information matrix is derived, and Monte Carlo studies are provided. We also illustrate the usefulness of the GARCH-type models with the AEPD and ASTD innovations in the context of predicting downside market risk of financial assets and demonstrate their superiority over skew-normal and skew-Student's t GARCH models. Finally, two new classes of generalized extreme value distributions, which include Jenkinson's GEV (Generalized Extreme Value) distribution (Jenkinson, 1955) as special cases, are proposed by using the maximum entropy principle, and their properties are investigated in detail.

We consider the use of a sieve bootstrap based on moving average (MA) and autoregressive moving average (ARMA) approximations to test the unit root hypothesis when the true Data Generating Process (DGP) is a general linear process. We provide invariance principles for these bootstrap DGPs and we prove that the resulting ADF tests are asymptotically valid. Our simulations indicate that these tests sometimes outperform those based on the usual autoregressive (AR) sieve bootstrap. We study the reasons for the failure of the AR sieve bootstrap tests and propose some solutions, including a modified version of the fast double bootstrap. / We also argue that using biased estimators to build bootstrap DGPs may result in less accurate inference. Some simulations confirm this in the case of ADF tests. We show that one can use the GLS transformation matrix to obtain equations that can be used to estimate bias in general ARMA(p,q) models. We compare the resulting bias reduced estimator to a widely used bootstrap based bias corrected estimator. Our simulations indicate that the former has better finite sample properties then the latter in the case of MA models. Finally, our simulations show that using bias corrected or bias reduced estimators to build bootstrap DGP sometimes provides accuracy gains.

The central theme of this dissertation is the development of a new approach to conceptualize and quantify dependence structures of capture-recapture data for closed populations, with specific emphasis on epidemiological applications. We introduce a measure of source dependence: the Coefficient of Incremental Dependence (CID). Properties of this and the related Coefficient of Source Dependence (CSD) of Vandal, Walker, and Pearson (2005) are presented, in particular their relationships to the conditional independence structures that can be modelled by hierarchical joint log-linear models (HJLLM). From these measures, we develop a new class of marginal log-linear models (MLLM), which we compare and contrast to HJLLMs. / We demonstrate that MLLMs serve to extend the universe of dependence structures of capture-recapture data that can be modelled and easily interpreted. Furthermore, the CIDs and CSDs enable us to meaningfully interpret the parameters of joint log-linear models previously excluded from the analysis of capture-recapture data for reasons of non-interpretability of model parameters. / In order to explore the challenges and features of MLLMs, we show how to produce inference from them under both a maximum likelihood and a Bayesian paradigm. The proposed modelling approach performs well and provides new insight into the fundamental nature of epidemiological capture-recapture data.

This thesis examines the development of modern statistical theory and its emergence as a highly specialised mathematical discipline at the end of the nineteenth century. The statistical work of the mathematician and statistician Karl Pearson (1857-1936), who almost singularly created the modern theory of statistics, is the focus of the thesis. The impact of the statistical and experimental work of the Darwinian zoologist W.F.R. Weldon (1860-1906), on the emergence and construction of Pearsonian statistical innovation, is central to the arguments developed in this thesis. Contributions to the Pearsonian corpus from such statisticians as Francis Ysidro Edgeworth (1845-1926), Francis Galton (1822-1911), and George Udny Yule (1871- 1951) are also addressed. The scope of the thesis does not involve a detailed account of every technical contribution that Pearson made to statistics. Instead, it provides a unifying assessment of Pearson's most seminal and innovative contributions to modern statistical theory devised in the Biometric School, at University College London, from 1892 to 1903. An assessment of Pearson's statistical contributions also entails a comprehensive examination of the two separate methodologies he developed in the Drapers' Biometric Laboratory (from 1903 to 1933) and in the Galton Eugenics Laboratory (from 1907 to 1933). This thesis arises, in part, from a desire to reassess the state of the historiography of Pearsonian statistics over the course of the last half century. Some of the earliest work on Pearson came from his former students who emphasised his achievements as a statistician usually from the perspective of the state of the discipline in their tune. The conventional view has presumed that Pearson's relationship with Galton and thus to Gallon's work on simple correlation, simple regression, inheritance and eugenics provided the impetus to Pearson's own statistical work. This approach, which focuses on a part of Pearson's statistical work, has provided minimal insight into the complexity of the totality of Pearsonian statistics. Another approach, derived from the sociology of knowledge in the 1970s, espoused this conventional view and linked Pearson's statistical work to eugenics by placing his work in a wider context of social and political ideologies. This has usually entailed frequent recourse to Pearson's social and political views vis-a-vis his popular writings on eugenics. This approach, whilst indicating the political and social dimensions of science, has produced a rather mono-causal or uni-dimensional view of history. The crucial question of the relation between his technical contributions and his ideology in the construction of his statistical methods has not yet been adequately considered. This thesis argues that the impetus to Pearson's earliest statistical work was given by his efforts to tackle the problems of asymmetrical biological distributions (arising from Weldon's dimorphic distribution of the female shore crab in the Bay of Naples). Furthermore, it argues that the fundamental developments and construction of Pearsonian statistics arose from the Darwinian biological concepts at the centre of Weldon's statistical and experimental work on marine organisms in Naples and in Plymouth. Charles Darwin's recognition that species comprised different sets of 'statistical' populations (rather than consisting of 'types' or 'essences') led to a reconceptualisation of statistical populations by Pearson and Weldon which, in turn, led to their attempts to find a statistical resolution of the pre-Darwinian Aristotelian essentialistic concept of species. Pearson's statistical developments thus involved a greater consideration of speciation and of Darwin's theory of natural selection than hitherto considered. This has, therefore, entailed a reconstruction of the totality of Pearsonian statistics to identify the mathematical and biological developments that underpinned his work and to determine other sources of influence in this development. Pearson's writings are voluminous: as principal author he published more than 540 papers and books of which 361 are statistical. The other publications include 67 literary and historical writings, 49 eugenics publications, 36 pure mathematics and physics papers and 27 reports on university matters. He also published at least 111 letters, notes and book reviews. His collected papers and letters at University College London consist of 235 boxes of family papers, scientific manuscripts and 14,000 letters. One of the most extensive sets of letters in the collection are those of W.F.R. Weldon and his wife, Florence Joy Weldon, which consists of nearly 1,000 pieces of correspondence. No published work on Pearson to date has properly utilised the correspondence between Pearson and the Weldons. Particular emphasis has been given to this collection as these letters indicate (in tandem with Pearson's Gresham lectures and the seminal statistical published papers) that Pearson's earliest statistical work started in 1892 (rather than 1895-1896) and that Weldon's influence and work during these years was decisive in the development and advancement of Pearsonian statistics. The approach adopted in this thesis is essentially that of an intellectual biography which is thematic and is broadly chronological. This approach has been adopted to make greater use of primary sources in an attempt to provide a more historically sensitive interpretation of Pearson's work than has been used previously. It has thus been possible to examine these three (as yet unexamined) key Pearsonian developments: (1) his earliest statistical work (from 1892 to 1895), (2) his joint biometrical projects with Weldon (from 1898-1906) and a shift in the focus of research in the Drapers' Biometric Laboratory following Weldon's death in 1906 and (3) the later work in the twentieth century when he established the two laboratories which were underpinned by two separate methodologies. The arguments, which follow a chronological progression, have been built around Darwin's ideas of biological variation, 'statistical' populations, his theory of natural selection and Galton's law of ancestral inheritance. The first two chapters provide background material to the arguments developed in the thesis. Weldon's use of correlation (for the identification of species) in 1889 is examined in Chaper III. It is argued, that Pearson's analysis of Weldon's dimorphic distribution led to their work on speciation which led on to Pearson's earliest innovative statistical work. Weldon's most productive research with Pearson, discussed in Chapter IV, came to fruition when he showed empirical evidence of natural selection by detecting disturbances (or deviations) in the distribution from normality as a consequence of differential mortality rates. This research enabled Pearson to further develop his theory of frequency distributions. The central part of the thesis broadens out to examine further issues not adequately examined. Galton's statistical approach to heredity is addressed in Chapter V, and it is shown that Galton adumbrated Pearson's work on multiple correlation and multiple regression with his law of ancestral heredity. This work, in conjunction with Weldon's work on natural selection, led to Pearson's introduction of the use of determinantal matrix algebra into statistical theory in 1896: this (much neglected) development was pivotal in the professionalisation of the emerging discipline of mathematical statistics. Pearson's work on goodness of fit testing provided the machinery for reconstructing his most comprehensive statistical work which spanned four decades and encompassed his entire working life as a statistician. Thus, a greater part of Pearsonian statistics has been examined than in previous studies.

Capture-recapture methods are used to estimate population size from overlapping, incomplete sources of information. With three or more sources, dependence between sources may be modelled using log-linear models. We propose a Coefficient of Incremental Dependence Criterion (CIDC) for selecting an estimate of population size among all possible estimates that result from hierarchical log-linear models. A penalty for the number of parameters in the model was selected via simulation for the three-source and four-source settings. The performance of the proposed criterion was compared to the Akaike Information Criterion (AIC) through simulation. The CIDC was found to modestly outperform the AIC for data generated from a population size of approximately 100, with AIC performing consistently better for larger population sizes. Modifications to the criterion such as incorporating the estimated population size and the type of source interaction present should be investigated, along with the mathematical properties of the CIDC.

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No description available.