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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<p>The 24-item scale has been used extensively to assess the attitudes towards AIDS precautions. This study investigated the usefulness and validity of the instrument in a South African setting, fourteen years after the development of the instrument. If a new structure could be found statistically, the HIV/AIDS prevention strategies could be more effective in aiding campaigns to change attitudes and sexual behaviour.</p>

Diversity indices confound two components: species richness and evenness. Community structure should therefore be evaluated by employing separate measures of the number of species and their relative abundances. However, the relative abundances of species are dependent on the abundance measure used. Although the use of biomass or productivity is recommended by theory, in practice a surrogate measure is more often used. Frequency (local or relative) and point-quadrat cover provide two objective measures of abundance which are fast, less destructive and avoid problems associated with distinguishing individuals. However, both give discrete bounded data which may further alter the relative abundances of species. These measures have a long history of use and, as the need for objective information on biodiversity becomes more pressing, their use is likely to become more widespread. Consequently, it seems appropriate to investigate the effect of these abundance measures, and the resolution at which they are used, on calculated evenness. Field, artificial and simulated data were used to investigate the effect of abundance measure and resolution on evidence for community structure. The field data consisted of seventeen sites. Sites from four vegetation types (saltmeadow, geothermal, ultramafic and high-altitude meadow) were sampled in three biogeographical regions. Most of the indices of community structure (species richness, diversity and evenness) detected differences between the different vegetation types, and different niche-apportionment models were fitted to the field data from saltmeadow and geothermal vegetation. Estimates of community structure based on local frequency and point-quadrat data differed. Local frequency tended to give higher calculated evenness; whereas point-quadrat data tended to fit to niche apportionment models where local frequency data failed. The effect of resolution on the eighteen evenness indices investigated depended on community species richness and the particular index used. The investigated evenness indices were divided into three groups (symmetric, continuous and traditional indices) based on how they ranked real and artificially constructed communities. Contrary to Smith and Wilson�s recommendation the symmetric indices E[VAR] and E[Q] proved unsuitable for use with most types of plant data. In particular, E[Q] tends to assign most communities low values and has a dubious relationship with intrinsic evenness. The continuous indices, E[MS] and E[2,1], were the indices best able to discriminate between field, artificial and simulated communities, and their use should be re-evaluated. Traditional indices used with low resolution tended to elevate the calculated evenness, especially in species-rich communities. The relativized indices, E[Hurlbert] and EO[dis], were an exception, as they were always able to attain the minimum of zero; however, they were more sensitive to changes in resolution, particularly when resolution was low. Overall, traditional indices based on Hill�s ratios, including E[1/D] (=E[2,0]), and G[2,1] gave the best performance, while the general criticism of the use of Pielou�s J� as an index of evenness was further substantiated by this study. As a final recommendation, ecologists are implored to investigate their data and the likely effects that sampling and analysis have had on the calculated values of their indices.

Diss. (sammanfattning) Uppsala : Sveriges lantbruksuniversitet, 2009. / Härtill 5 uppsatser.

Orientador: Sheila Zambello de Pinho / Banca: Martha Maria Mischan / Banca: Décio Barbin / Banca: Antonio Francisco Iemma / Banca: David Ariovaldo Banzatto / Resumo: As funções de crescimento logística e de Gompertz têm sido bastante estudadas e freqüentemente utilizadas na área biológica. Diversos pesquisadores têm ajustado as funções logística ou de Gompertz a dados provenientes de experimentos com vários tratamentos onde curvas são ajustadas e o interesse é saber se há diferença entre estes tratamentos. A verificação da adequacidade de ajustes das funções não-lineares e a comparação de diferentes funções para um determinado conjunto de dados estão bem contempladas na literatura. Porém, quando o mesmo tipo de função é ajustado a várias situações (tratamentos) e o interesse é fazer a comparação das mesmas, há dificuldades de se encontrar subsídios na literatura. O objetivo deste trabalho foi a apresentação de um método de comparação de curvas logísticas e de Gompertz. Compararam-se as equações ajustadas através de testes dos parâmetros, utilizando-se métodos paramétricos e nãoparamétricos. Determinaram-se também, valores da variável independente x a partir dos quais a diferença entre a assíntota e a curva ajustada deixa de ser significativa. Estudaram-se nesta pesquisa o modelo logístico com erro aditivo na ausência e na presença de autocorrelação nos resíduos, o modelo logístico com erro multiplicativo na ausência e na presença de autocorrelação nos resíduos, o modelo de Gompertz com erro aditivo na ausência e na presença de autocorrelação nos resíduos e o modelo de Gompertz com erro multiplicativo na ausência e na presença de autocorrelação nos resíduos. Para ilustração da metodologia utilizaram-se dados de peso de matéria fresca (g) de sementes de feijão Phaseolus vulgaris L. cv. carioca 80 SH, porcentagens médias do peso de frutos de araribá, pesos de frangos de corte de aves Indian River e pesos de ratos Rattus norvergicus, aos quais ajustaram-se,...(Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The logistic and the Gompertz growth functions have been considerably studied and frequently used in biological area. Several researchers have fitted the Logistic and the Gompertz to data from experiments with many treatments where the purpose is to detect the difference among them. The verification of the adequacy of the non-linear fits and the comparison of different functions for a set of data are well studied in the literature. However, when the same function is fitted to several situations (treatments) and the purpose is to compare them, there are difficulty to find subsidy in the literature. The purpose of this work was to determine a method of comparison of the Logistic and the Gompertz curves and to verify until when the difference between the curves and their superior asymptotes are significant. In this research were studied the logistic and the Gompertz models considering additive and multiplicative error terms with and without autocorrelation. For enlightenment of the methodology were used data of fresh matter of Phaseolus vulgaris L. cv carioca 80 SH seeds, percentage of araribá fruit weight, weight of chicken for slaughter Indian River and weight of rats Rattus norvergicus, where were fitted the Logistic model with additive errors terms and without autocorrelation, the Logistic model with additive errors terms and with autocorrelation, the Gompertz model with additive errors terms and without autocorrelation, the Gompertz model with additive errors terms and with autocorrelation...(Complete abstract, click electronic access below) / Doutor