My final thesis firstly addresses basic knowledge of the theory of stochastic processes. This is firstly due to the author's effort to make the thesis more comprehensible, and also due to the need for introduction of key concepts. The autoregressive model AR(1) is defined in the thesis through basic linear time series models, and in this model, the estimation of model parameter by the method of least squares is introduced. For this estimation, the theoretical findings of the thesis are extended through the classical limit theory. Furthermore, the models with their parameter dependent on number of observations are introduced and models of NIAR (1) are defined. Classical limit theory for least squares estimation is then enriched by the limit theory in these models. The category of more general models is introduced and using the acquired knowledge, the features for the model AR (1) are derived. This thesis deals with this issue in models of NIAR (1) and its area of interest is also the bootstrap. The theoretical part of the thesis is supplemented by a practical part represented by numerical studies.

Master of Science / Department of Statistics / Weixing Song / A robust estimation procedure for mixture linear regression models is proposed in this report by assuming the error terms follow a Laplace distribution. EM algorithm is imple- mented to conduct the estimation procedure of missing information based on the fact that the Laplace distribution is a scale mixture of normal and a latent distribution. Finite sample performance of the proposed algorithm is evaluated by some extensive simulation studies, together with the comparisons made with other existing procedures in this literature. A sensitivity study is also conducted based on a real data example to illustrate the application of the proposed method.

By testing a fiber beard, certain cotton fiber length parameters can be obtained rapidly. This is the method used by the High Volume Instrument (HVI). This study is aimed to explore the approaches and obtain the inference of length distributions of HVI beard sam- ples in order to develop new methods that can help us find the distribution of original fiber lengths and further improve HVI length measurements. At first, the mathematical functions were searched for describing three different types of length distributions related to the beard method as used in HVI: cotton fiber lengths of the original fiber population before picked by the HVI Fibrosampler, fiber lengths picked by HVI Fibrosampler, and fiber beard's pro-jecting portion that is actually scanned by HVI. Eight sets of cotton samples with a wide range of fiber lengths are selected and tested on the Advanced Fiber Information System (AFIS). The measured single fiber length data is used for finding the underlying theoreti-cal length distributions, and thus can be considered as the population distributions of the cotton samples. In addition, fiber length distributions by number and by weight are dis- cussed separately. In both cases a mixture of two Weibull distributions shows a good fit to their fiber length data. To confirm the findings, Kolmogorov-Smirnov goodness-of-fit tests were conducted. Furthermore, various length parameters such as Mean Length (ML) and Upper Half Mean Length (UHML) are compared between the original distribution from the experimental data and the fitted distributions. The results of these obtained fiber length distributions are discussed by using Partial Least Squares (PLS) regression, where the dis-tribution of the original fiber length from the distribution of the projected one is estimated.

The matrix-inversion-lemma based recursive least squares (RLS) approach is of a recursive form and free of matrix inversion, and has excellent performance regarding computation and memory in solving the classic least-squares (LS) problem. It is important to generalize RLS for generalized LS (GLS) problem. It is also of value to develop an efficient initialization for any RLS algorithm. In Chapter 2, we develop a unified RLS procedure to solve the unconstrained/linear-equality (LE) constrained GLS. We also show that the LE constraint is in essence a set of special error-free observations and further consider the GLS with implicit LE constraint in observations (ILE-constrained GLS). Chapter 3 treats the RLS initialization-related issues, including rank check, a convenient method to compute the involved matrix inverse/pseudoinverse, and resolution of underdetermined systems. Based on auxiliary-observations, the RLS recursion can start from the first real observation and possible LE constraints are also imposed recursively. The rank of the system is checked implicitly. If the rank is deficient, a set of refined non-redundant observations is determined alternatively. In Chapter 4, base on [Li07], we show that the linear minimum mean square error (LMMSE) estimator, as well as the optimal Kalman filter (KF) considering various correlations, can be calculated from solving an equivalent GLS using the unified RLS. In Chapters 5 & 6, an approach of joint state-and-parameter estimation (JSPE) in power system monitored by synchrophasors is adopted, where the original nonlinear parameter problem is reformulated as two loosely-coupled linear subproblems: state tracking and parameter tracking. Chapter 5 deals with the state tracking which determines the voltages in JSPE, where dynamic behavior of voltages under possible abrupt changes is studied. Chapter 6 focuses on the subproblem of parameter tracking in JSPE, where a new prediction model for parameters with moving means is introduced. Adaptive filters are developed for the above two subproblems, respectively, and both filters are based on the optimal KF accounting for various correlations. Simulations indicate that the proposed approach yields accurate parameter estimates and improves the accuracy of the state estimation, compared with existing methods.

Approved for public release; distribution is unlimited / Computer simulation studies of a frequency domain adaptive beamforming algorithm are presented. These simulation studies were conducted to determine the multiple broadband target localization capability and the full angular coverage capability of the algorithm. The algorithm was evaluated at several signal-to-noise ratios with varying sampling rates. The number of iterations that the adaptive algorithm took to reach a minimum estimation error was determined. Results of the simulation studies indicate that the algorithm can localize multiple broadband targets and has full angular coverage capability. / http://archive.org/details/computersimulati00behr / Lieutenant, United States Navy

[pt] Este trabalho busca reconstruir a geometria de uma malha partindo de sua conectividade e de um conjunto esparso de pontos com geometria conhecida, denominados pontos de controle. O problema é formulado como a maximização da suavidade da superfície fixando a posição dos pontos de controle. Nessa formulação, o método consiste em resolver um sistema linear esparso aplicando-se mínimos quadrados. Diferentes propostas para a seleção de pontos de controle, o método de minimização e a construção do sistema linear são apresentadas e comparadas. / [en] This work aims at reconstructing the geometry of a mesh from its connectivity and a small set of control points, whose geometry is known.The problem is formulated as a maximization of the surface smoothness restricting the position of the control points. With this formulation, the method reduces to solving a sparse linear system using least squares minimization. Several proposals for the selection of the control points, the minimization method and the linear system construction are presented and compared .

This thesis is concerned with the issue of the regularization of the Recursive Least-Squares (RLS) algorithm. In the first part of the thesis, a novel regularized exponentially weighted array RLS algorithm is developed, which circumvents the problem of fading regularization that is inherent to the standard regularized exponentially weighted RLS formulation, while allowing the employment of generic time-varying regularization matrices. The standard equations are directly perturbed via a chosen regularization matrix; then the resulting recursions are extended to the array form. The price paid is an increase in computational complexity, which becomes cubic. The superiority of the algorithm with respect to alternative algorithms is demonstrated via simulations in the context of adaptive beamforming, in which low filter orders are employed, so that complexity is not an issue. In the second part of the thesis, an alternative criterion is motivated and proposed for the dynamical regulation of regularization in the context of the standard RLS algorithm. The regularization is implicitely achieved via dithering of the input signal. The proposed criterion is of general applicability and aims at achieving a balance between the accuracy of the numerical solution of a perturbed linear system of equations and its distance from the analytical solution of the original system, for a given computational precision. Simulations show that the proposed criterion can be effectively used for the compensation of large condition numbers, small finite precisions and unecessary large values of the regularization. / Esta tese trata da regularização do algoritmo dos mínimos-quadrados recursivo (Recursive Least-Squares - RLS). Na primeira parte do trabalho, um novo algoritmo array com matriz de regularização genérica e com ponderação dos dados exponencialmente decrescente no tempo é apresentado. O algoritmo é regularizado via perturbação direta da inversa da matriz de auto-correlação (Pi) por uma matriz genérica. Posteriormente, as equações recursivas são colocadas na forma array através de transformações unitárias. O preço a ser pago é o aumento na complexidade computacional, que passa a ser de ordem cúbica. A robustez do algoritmo resultante ´e demonstrada via simula¸coes quando comparado com algoritmos alternativos existentes na literatura no contexto de beamforming adaptativo, no qual geralmente filtros com ordem pequena sao empregados, e complexidade computacional deixa de ser fator relevante. Na segunda parte do trabalho, um critério alternativo ´e motivado e proposto para ajuste dinâmico da regularização do algoritmo RLS convencional. A regularização é implementada pela adição de ruído branco no sinal de entrada (dithering), cuja variância é controlada por um algoritmo simples que explora o critério proposto. O novo critério pode ser aplicado a diversas situações; procura-se alcançar um balanço entre a precisão numérica da solução de um sistema linear de equações perturbado e sua distância da solução do sistema original não-perturbado, para uma dada precisão. As simulações mostram que tal critério pode ser efetivamente empregado para compensação de números de condicionamento (CN) elevados, baixa precisão numérica, bem como valores de regularização excessivamente elevados.

Inom bank och försäkringsbranschen finns behov av framtidsprognoser och riskmått kopplade till finansiella instrument. För att skapa prisfördelningar, som kan användas som grund till olika riskmått, används ibland nästlad simulering. För att göra detta simuleras först en stor mängd yttre scenarion för någon tillgång, som används i ett finanisellt instrument. Vilket görs genom att priser simuleras över en tidsperiod. Detta utgör tidshorisonten varvid prisfördelningen befinner sig. Utifrån varje yttre scenario simuleras sedan ett antal inre. Som i sin tur används för att prissätta finansiella instrumentet i det yttre scenariot. En metod som används för att prisätta de yttre scenariona är Monte Carlo-metoden, vilket kräver ett stort antal inre scenarion för att prissättningen ska bli korrekt. Detta gör metoden krävande i tidsåtgång och datorkraft. Least Squares Monte Carlo-metoden är en alternativ metod som använder sig av regression och minstakvadratmetoden för att utföra prissättningen med ett mindre antal inre scenarion. En regressionsfunktion anpassas efter yttre scenarionas värden och används sedan för att omvärdera dessa, vilket minskar felen som ett mindre antal slumptal annars skulle ge. Regressionsfunktionen kan även användas för att prissätta värden utanför de som den anpassas efter, vilket gör att den kan återanvändas vid liknande beräkningar. I detta arbete undersöks hur väl Least Squares Monte Carlo-metoden beskriver prisfördelningen för korgoptioner, som är optioner med flera underliggande tillgångar. Tester utförs med olika värden för parametrarna och vikt läggs vid vilken effekt yttre scenarionas längd har, samt hur väl priserna beskrivs i prisfördelningens svansar. Resultatet är delvis svåranalyserat på grund av många extrema värden, men visade på svårigheter med prissättningen vid längre yttre scenarion. Vilket kan bero på att regressionsfunktionen som användes hade svårt att anpassa sig efter och beskriva mer spridda prisfördelningar. Metoden fungerade också sämre i den nedre delen av prisfördelningen, något som den dock delar med Standard Monte Carlo. Mer forskning behövs för att undersöka vilken effekt andra uppsättningar regressionsfunktioner skulle ha på metoden. / In the banking and insurance industry, there exists a need for forecasting and measures of risk connecting to financial instruments. To create price distributions, used to create measures of risk, nested simulations are sometimes used. This is done by simulating a large amount of outer scenarios, for some asset in a financial instrument. Which is done by simulating prices over a certain time period. This now outlines the time horizon of the price distribution. From each outer scenario, some inner scenarios are simulated. Which in turn are used to price the financial instrument in the outer scenario. A common method for pricing the outer scenarios is the Monte Carlo method, which uses a large amount of random numbers for the pricing to be accurate. This makes the method time consuming, as well as requiring large amounts of computing power. The Least Squares Monte Carlo method is an alternative method, using regression and the least squares method to perform the pricing using a smaller amount of inner scenarios. A regression function is fitted to the values of the outer scenarios and then used to revalue these, reducing the error which a smaller number of random numbers otherwise would give. The regression function can also be used to price outside of the values used for the fitting, making it reusable in similar computations. This paper examines how well the Least Squares Monte Carlo-method describes the price distribution of basket options, which are options containing several underlying assets. Tests are made for different values for the parameters used and an emphasis is laid on the effect of the time length of the outer scenarios, also, how accurate the tails of the distribution are. The results are somewhat hard to analyze,due to some extreme values, but showed difficulties for the method, when pricing longer outer scenarios. This can be due to the regression function having problems fitting to - and valuing - broader price distributions. The method also performed worse in the lower parts of the distribution, something it shares with the standard Monte Carlo method. More research is needed to ascertain the effects of other regression functions.

Made available in DSpace on 2016-07-27T13:49:23Z (GMT). No. of bitstreams: 1 FRANCISCO ALBERTIN FERREIRA.pdf: 708318 bytes, checksum: 19f78ea9054dd3ba7002710a07f78b01 (MD5) Previous issue date: 2006-08-29 / The present dissertation discusses the Last Judgment that is a current theme of investigation. This is due to the fact that the three major monotheistic religions approach it in their religious essence. In judaism, it is related to the acts of piety present in the Old Testament; in christianity, to acts of mercy which involve a compromise of love to God and neighbor and are fundamental for obtaining salvation; and, in Islam, the good or evil that one practices with his brothers are important acts for either gaining paradise or ending in hell. In the first part, the question of text in its context is approached: the social reality of the Roman Empire, of the judeo-christian community, in Antiocus, and the necessity of solidarity that this text expresses. In the second part, there is a complete exegesis in all its steps to the Last Judgment (Matthew 25,31-46), within these, there is the delineation, the structure, the linguistic configuration, the wording, the characteristics of God present in the text and much other exegetical informations. In the third part, the updating of the message of the Last Judgment is presented which has, as its base, three dimensions: the personal, ecclesiastical and social, where, according to Jesus teachings, the acts of mercy, practiced in relation to the least of God s creature, here and now, will be decisive at the Last Judgment, when the Son of Man will judge each according to his acts. / A presente dissertação discorre sobre o Juízo Final que é um tema atual e questionador. Isto se deve ao fato das três grandes religiões monoteístas o abordarem em sua essência religiosa. No judaísmo, está relacionado às obras de piedade presentes no Antigo Testamento; no cristianismo, às obras de misericórdia que envolvem compromisso de amor a Deus e ao próximo e são fundamentais para se obter a salvação; e, no islamismo, o bem ou mal que se pratica com os irmãos são obras importantes para possuir o paraíso ou acabar no inferno. Na primeira parte, é abordada a questão do texto em seu contexto: a realidade social do Império Romano, da comunidade judaico-cristã, na Antioquia, e a necessidade da solidariedade que este texto expressa. Na segunda parte, há uma exegese completa em todos os seus passos sobre o Juízo Final (Mateus 25,31-46), dentre estes, a delimitação, a estrutura, a configuração lingüística, a redação, as características de Deus existentes no texto e muitas outras informações exegéticas. Na terceira parte, é apresentada a atualização da mensagem do Juízo Final que tem, por base, três dimensões: pessoal, eclesial e social, onde, de acordo com os ensinamentos de Jesus, as obras de misericórdia, praticadas em relação aos mais pequeninos, aqui e agora, serão decisivas no dia do Juízo Final, quando o Filho do Homem julgará cada um de acordo com suas obras.

by Ho King Choi. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1991. / Includes bibliographical references. / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Adaptive Filter and Adaptive System --- p.1 / Chapter 1.2 --- Applications of Adaptive Filter --- p.4 / Chapter 1.2.1 --- System Identification --- p.4 / Chapter 1.2.2 --- Noise Cancellation --- p.6 / Chapter 1.2.3 --- Echo Cancellation --- p.8 / Chapter 1.2.4 --- Speech Processing --- p.10 / Chapter 1.3 --- Chapter Summary --- p.14 / References --- p.15 / Chapter 2. --- Adaptive Filter Structures and Algorithms --- p.17 / Chapter 2.1 --- Filter Structures for Adaptive Filtering --- p.17 / Chapter 2.2 --- Adaptation Algorithms --- p.22 / Chapter 2.2.1 --- The LMS Adaptation Algorithm --- p.24 / Chapter 2.2.1.1 --- Convergence Analysis --- p.28 / Chapter 2.2.1.2 --- Steady State Performance --- p.33 / Chapter 2.2.2 --- The RLS Adaptation Algorithm --- p.35 / Chapter 2.3 --- Chapter Summary --- p.39 / References --- p.41 / Chapter 3. --- Parallel Split Adaptive System --- p.45 / Chapter 3.1 --- Parallel Form Adaptive Filter --- p.45 / Chapter 3.2 --- Joint Process Estimation with a Split-Path Adaptive Filter --- p.49 / Chapter 3.2.1 --- The New Adaptive System Identification Configuration --- p.53 / Chapter 3.2.2 --- Analysis of the Split-Path System Modeling Structure --- p.57 / Chapter 3.2.3 --- Comparison with the Non-Split Configuration --- p.63 / Chapter 3.2.4 --- Some Notes on Even Filter Order Case --- p.67 / Chapter 3.2.5 --- Simulation Results --- p.70 / Chapter 3.3 --- Autoregressive Modeling with a Split-Path Adaptive Filter --- p.75 / Chapter 3.3.1 --- The Split-Path Adaptive Filter for AR Modeling --- p.79 / Chapter 3.3.2 --- Analysis of the Split-Path AR Modeling Structure --- p.84 / Chapter 3.3.3 --- Comparison with Traditional AR Modeling System --- p.89 / Chapter 3.3.4 --- Selection of Step Sizes --- p.90 / Chapter 3.3.5 --- Some Notes on Odd Filter Order Case --- p.94 / Chapter 3.3.6 --- Simulation Results --- p.94 / Chapter 3.3.7 --- Application to Noise Cancellation --- p.99 / Chapter 3.4 --- Chapter Summary --- p.107 / References --- p.109 / Chapter 4. --- Serial Split Adaptive System --- p.112 / Chapter 4.1 --- Serial Form Adaptive Filter --- p.112 / Chapter 4.2 --- Time Delay Estimation with a Serial Split Adaptive Filter --- p.125 / Chapter 4.2.1 --- Adaptive TDE --- p.125 / Chapter 4.2.2 --- Split Filter Approach to Adaptive TDE --- p.132 / Chapter 4.2.3 --- Analysis of the New TDE System --- p.136 / Chapter 4.2.3.1 --- Least-mean-square Solution --- p.138 / Chapter 4.2.3.2 --- Adaptation Algorithm and Performance Evaluation --- p.142 / Chapter 4.2.4 --- Comparison with Traditional Adaptive TDE Method --- p.147 / Chapter 4.2.5 --- System Implementation --- p.148 / Chapter 4.2.6 --- Simulation Results --- p.148 / Chapter 4.2.7 --- Constrained Adaptation for the New TDE System --- p.156 / Chapter 4.3 --- Chapter Summary --- p.163 / References --- p.165 / Chapter 5. --- Extension of the Split Adaptive Systems --- p.167 / Chapter 5.1 --- The Generalized Parallel Split System --- p.167 / Chapter 5.2 --- The Generalized Serial Split System --- p.170 / Chapter 5.3 --- Comparison between the Parallel and the Serial Split Adaptive System --- p.172 / Chapter 5.4 --- Integration of the Two Forms of Split Predictors --- p.177 / Chapter 5.5 --- Application of the Integrated Split Model to Speech Encoding --- p.179 / Chapter 5.6 --- Chapter Summary --- p.188 / References --- p.139 / Chapter 6. --- Conclusions --- p.191 / References --- p.197