Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 114-117). Also available on the Internet.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 213-219).

Thesis (Ph. D.)--University of California, San Diego, 2009. / Title from first page of PDF file (viewed July 23, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 104-109).

The main subject of this thesis is a change point detection in stationary vector autoregressions. Various test statistics are proposed for the retrospective break point detection in the parameters of such models, in particular, the derivation of their asymptotic distribution under the null hypothesis of no change. Testing procedures are based on the maximum like- lihood principle and are derived under normality, nevertheless the asymptotic results are valid for broader class of distributions and involve also the models with certain form of dependence. Simulation studies document the quality of the results.

No description available.

São estudadas flutuações de variáveis spin de bloco em alguns modelos de Curie-Weiss. É descrito rigorosamente o comportamento assintótico de suas distribuições de probabilidade no limite termodinâmico, mantendo constante a razão entre o tamanho do sistema e o tamanho do bloco. São considerados o modelo de Ising com campo aleatório e o antiferromagneto diluído. Os seguintes fatos sobre flutuações nestes modelos são provados: a) Elas não são auto-mediantes; b) Fora da criticalidade têm distribuição Gaussiana com contribuições vindas de flutuações térmicas e de flutuações devidas aos parâmetros aleatórios; c) Na criticalidade a sua distribuição e não mais Gaussiana e as flutuações das impurezas dominam as flutuações térmicas. Como sub-produto desta análise mostra-se que as flutuações destes dois modelos não são equivalentes sob o mapeamento que estabelece a sua equivalência termodinâmica. Também é descrita a aplicação do método ao vidro de spin de van Hemmen, sem provas, levando a resultados similares. Finalmente mostra-se que o método é problemático quando aplicado a sistemas quânticos. Embora a sua termodinâmica possa ser bem descrita, aparecem alguns problemas matemáticos, ainda por resolver, no estudo das suas flutuações. / Fluctuations of block spin variables in some Curie-Weiss models are studied. The asymptotic behavior of their probability distributions in the thermodynamic limit is rigorously described, keeping constant the ratio between the size of the system and the size of the block. The Ising model with random field and the dilute antiferromagnet with uniform field are considered. The following facts about fluctuations in these models are proved: a) They are not self-averaging; b) Out of criticality they have a Gaussian distribution with contributions coming both from thermal fluctuations and from those fluctuations due to the random parameters; c) At criticality their distribution is no longer Gaussian and the fluctuation of impurities dominate thermal fluctuations. As a by-product of this analysis, the fluctuations of these two models are shown to be non-equivalent under the mapping which establishes their thermodynamical equivalence. It is also described the application of the method to the van Hemmen spin-glass model, without proofs, leading to similar results. Finally the method is shown to be problematic when applied to quantum systems. Although their thermodynamics can be well described, some mathematical problems, yet to be solved, appear in the study of their fluctuations.

São estudadas flutuações de variáveis spin de bloco em alguns modelos de Curie-Weiss. É descrito rigorosamente o comportamento assintótico de suas distribuições de probabilidade no limite termodinâmico, mantendo constante a razão entre o tamanho do sistema e o tamanho do bloco. São considerados o modelo de Ising com campo aleatório e o antiferromagneto diluído. Os seguintes fatos sobre flutuações nestes modelos são provados: a) Elas não são auto-mediantes; b) Fora da criticalidade têm distribuição Gaussiana com contribuições vindas de flutuações térmicas e de flutuações devidas aos parâmetros aleatórios; c) Na criticalidade a sua distribuição e não mais Gaussiana e as flutuações das impurezas dominam as flutuações térmicas. Como sub-produto desta análise mostra-se que as flutuações destes dois modelos não são equivalentes sob o mapeamento que estabelece a sua equivalência termodinâmica. Também é descrita a aplicação do método ao vidro de spin de van Hemmen, sem provas, levando a resultados similares. Finalmente mostra-se que o método é problemático quando aplicado a sistemas quânticos. Embora a sua termodinâmica possa ser bem descrita, aparecem alguns problemas matemáticos, ainda por resolver, no estudo das suas flutuações. / Fluctuations of block spin variables in some Curie-Weiss models are studied. The asymptotic behavior of their probability distributions in the thermodynamic limit is rigorously described, keeping constant the ratio between the size of the system and the size of the block. The Ising model with random field and the dilute antiferromagnet with uniform field are considered. The following facts about fluctuations in these models are proved: a) They are not self-averaging; b) Out of criticality they have a Gaussian distribution with contributions coming both from thermal fluctuations and from those fluctuations due to the random parameters; c) At criticality their distribution is no longer Gaussian and the fluctuation of impurities dominate thermal fluctuations. As a by-product of this analysis, the fluctuations of these two models are shown to be non-equivalent under the mapping which establishes their thermodynamical equivalence. It is also described the application of the method to the van Hemmen spin-glass model, without proofs, leading to similar results. Finally the method is shown to be problematic when applied to quantum systems. Although their thermodynamics can be well described, some mathematical problems, yet to be solved, appear in the study of their fluctuations.

The limiting law of the length of the longest increasing subsequence, LI_n, for sequences (words) of length n arising from iid letters drawn from finite, ordered alphabets is studied using a straightforward Brownian functional approach. Building on the insights gained in both the uniform and non-uniform iid cases, this approach is then applied to iid countable alphabets. Some partial results associated with the extension to independent, growing alphabets are also given. Returning again to the finite setting, and keeping with the same Brownian formalism, a generalization is then made to words arising from irreducible, aperiodic, time-homogeneous Markov chains on a finite, ordered alphabet. At the same time, the probabilistic object, LI_n, is simultaneously generalized to the shape of the associated Young tableau given by the well-known RSK-correspondence. Our results on this limiting shape describe, in detail, precisely when the limiting shape of the Young tableau is (up to scaling) that of the iid case, thereby answering a conjecture of Kuperberg. These results are based heavily on an analysis of the covariance structure of an m-dimensional Brownian motion and the precise form of the Brownian functionals. Finally, in both the iid and more general Markovian cases, connections to the limiting laws of the spectrum of certain random matrices associated with the Gaussian Unitary Ensemble (GUE) are explored.

We consider the problem of estimating the failure stresses of bundles (i.e. the tensile forces that destroy the bundles), constructed of several statisti-cally similar fibres, given a particular kind of censored data. Each bundle consists of several fibres which have their own independent identically dis-tributed failure stresses, and where the force applied on a bundle at any moment is distributed equally between the unbroken fibres in the bundle. A bundle with these properties is an example of an equal load-sharing sys-tem, often referred to as the Daniels failure model. The testing of several bundles generates a special kind of censored data, which is complexly struc-tured. Strongly consistent non-parametric estimators of the distribution laws of bundles are obtained by applying the theory of martingales, and by using the observed data. It is proved that random sampling, with replace-ment from the statistical data related to each tested bundle, can be used to obtain asymptotically correct estimators for the distribution functions of deviations of non-parametric estimators from true values. In the case when the failure stresses of the fibres are described by a Weibull distribution, we obtain strongly consistent parametric maximum likelihood estimators of the distribution functions of failure stresses of bundles, by using the complexly structured data. Numerical examples illustrate the behavior of the obtained estimators.

This thesis concerns the problem of statistical hypothesis testing for mean vector as well as testing for non-normality in a high-dimensional setting which is called the Kolmogorov condition. Since we consider mainly the first and the second moment in testing for mean vector and we utilize the third and the fourth moment in testing for non-normality, this thesis concerns a more general moment testing problem. The research question is related to a data matrix with $p$ rows, which is the number of parameters and $n$ columns which is the sample size, where $p$ can exceed $n$, assuming that the ratio $\frac{p}{n}$ converges when both the number of parameters and the sample size increase.  The first paper reviews the Dempster's non-exact test for mean vector, with a focus on one-sample case. We investigated its size and power properties compared to Hotelling's $\mathit{T}^2$ test as well as Srivastava's test using Monte Carlo simulation.  The second paper concerns the problem of testing for multivariate non-normality in high-dimensional data. We proposed three test statistics which are based on marginal skewness and kurtosis. Simulation studies are carried out for examining the size and power properties of the three test statistics. / Avhandlingen undersöker hypotesprövning i höga dimensioner, under förutsättning att det så kallad Kolmogorovvillkoret (Kolmogorov condition) är uppfyllt. Villkoret innerbär att antalet parametrar ökar tillsammans med storleken på stickprovet med en konstant hastighet. Till kategorin multivariat analys räknas de statistiska metoder som analyserar stickprov från flerdimensionella fördelningar, särskilt multivariat normalfördelning. För högdimensionella data fungerar klassiska skattningar av kovariansmatris inte tillfredställande eftersom komplexiteten med att skatta den inversa kovariansmatrisen ökar när dimensionen ökar. I den första uppsatsen utförs en genomgång av Dempsters (non-exact) test där skattning av den inversa kovariansmatrisen inte behövs. Istället används spåret (trace) av en kovariansmatris. I den andra uppsatsen testas antagandet om normalfördelning med hjälp av tredje och fjärde ordningens moment. Tre olika testvariabler har föreslagits där sumuleringar också presenteras för att jämföra hur väl en icke-normalfördelning identifieras av testet.