Penalized methods are becoming more and more popular in statistical research. This dissertation research covers two major aspects of applications of penalized methods: variable selection and nonparametric function estimation. The following two paragraphs give brief introductions to each of the two topics. Infinite variance autoregressive models are important for modeling heavy-tailed time series. We use a penalty method to conduct model selection for autoregressive models with innovations in the domain of attraction of a stable law indexed by alpha is an element of (0, 2). We show that by combining the least absolute deviation loss function and the adaptive lasso penalty, we can consistently identify the true model. At the same time, the resulting coefficient estimator converges at a rate of n^(?1/alpha) . The proposed approach gives a unified variable selection procedure for both the finite and infinite variance autoregressive models. While automatic smoothing parameter selection for nonparametric function estimation has been extensively researched for independent data, it is much less so for clustered and longitudinal data. Although leave-subject-out cross-validation (CV) has been widely used, its theoretical property is unknown and its minimization is computationally expensive, especially when there are multiple smoothing parameters. By focusing on penalized modeling methods, we show that leave-subject-out CV is optimal in that its minimization is asymptotically equivalent to the minimization of the true loss function. We develop an efficient Newton-type algorithm to compute the smoothing parameters that minimize the CV criterion. Furthermore, we derive one simplification of the leave-subject-out CV, which leads to a more efficient algorithm for selecting the smoothing parameters. We show that the simplified version of CV criteria is asymptotically equivalent to the unsimplified one and thus enjoys the same optimality property. This CV criterion also provides a completely data driven approach to select working covariance structure using generalized estimating equations in longitudinal data analysis. Our results are applicable to additive, linear varying-coefficient, nonlinear models with data from exponential families.

This thesis analyzes the process of deblurring of degraded images generated by space-variant nonlinear image systems with Gaussian observation noise. The restoration of blurred images is performed by using two methods / a modified version of the Optimum Decoding Based Smoothing Algorithm and the Bootstrap Filter Algorithm which is a version of Particle Filtering methods. A computer software called MATLAB is used for performing the simulations of image estimation. The results of some simulations for various observation and image models are presented.

Incremental smoothing and mapping (iSAM) is presented, a novel approach to the simultaneous localization and mapping (SLAM) problem. SLAM is the problem of estimating an observer's position from local measurements only, while creating a consistent map of the environment. The problem is difficult because even very small errors in the local measurements accumulate over time and lead to large global errors. iSAM provides an exact and efficient solution to the SLAM estimation problem while also addressing data association. For the estimation problem, iSAM provides an exact solution by performing smoothing, which keeps all previous poses as part of the estimation problem, and therefore avoids linearization errors. iSAM uses methods from sparse linear algebra to provide an efficient incremental solution. In particular, iSAM deploys a direct equation solver based on QR matrix factorization of the naturally sparse smoothing information matrix. Instead of refactoring the matrix whenever new measurements arrive, only the entries of the factor matrix that actually change are calculated. iSAM is efficient even for robot trajectories with many loops as it performs periodic variable reordering to avoid unnecessary fill-in in the factor matrix. For the data association problem, I present state of the art data association techniques in the context of iSAM and present an efficient algorithm to obtain the necessary estimation uncertainties in real-time based on the factored information matrix. I systematically evaluate the components of iSAM as well as the overall algorithm using various simulated and real-world data sets.

Διάφορες κλιματολογικές, υδρολογικές και περιβαλλοντικές μελέτες απαιτούν ακριβή γνώση της χωρικής κατανομής των σταθερών ισοτόπων του υδρογόνου και του οξυγόνου στον υετό. Δεδομένου ότι ο αριθμός των σταθμών συλλογής δειγμάτων υετού για ισοτοπική ανάλυση είναι μικρός και όχι ομογενώς κατανεμημένος σε πλανητικό επίπεδο, η πλανητκή κατανομή των σταθερών ισοτόπων μπορεί να υπολογισθεί μέσω της δημιουργίας πλεγματικών ισοτοπικών δεδομένων, για τη δημιουργία των οποίων έχουν προταθεί διάφορες μέθοδοι. Ορισμένες χρησιμοποιούν εμπειρικές σχέσεις και γεωστατιστικές μεθόδους ώστε να ελαχιστοποιήσουν τα σφάλματα λόγω παρεμβολής. Στην εργασία αυτή γίνεται μια προσπάθεια να δημιουργηθούν βάσεις πλεγματικών δεδομένων της ισοτοπικής σύστασης του υετού με ανάλυση 10΄ × 10΄ για την περιοχή της Κεντρικής και Ανατολικής Μεσογείου. Προσδιορίζονται στατιστικά πρότυπα λαμβάνοντας υπ’ όψιν γεωγραφικές και μετεωρολογικές παραμέτρους, ως ανεξάρτητες μεταβλητές. Η αρχική μεθοδολογία χρησιμοποιεί μόνο το υψόμετρο της περιοχής και το γεωγραφικό της πλάτος ως ανεξάρτητες μεταβλητές. Επειδή η ισοτοπική σύσταση εξαρτάται και από το γεωγραφικό μήκος προστέθηκαν στα υφιστάμενα πρότυπα, εκτός των γεωγραφικών μεταβλητών και μετεωρολογικές. Προτείνεται σειρά προτύπων τα οποία περιλαμβάνουν είτε ορισμένες είτε συνδυασμό αυτών των παραμέτρων. Η αξιολόγηση των προτύπων γίνεται με εφαρμογή των μεθόδων Thin Plate Splines (TPSS) και Ordinary Kriging (ΟΚ). / Several climatic, hydrological and environmental studies require the accurate knowledge of the spatial distribution of stable isotopes in precipitation. Since the number of rain sampling stations for isotope analysis is small and not evenly distributed around the globe, the global distribution of stable isotopes can be calculated via the production of gridded isotopic data sets. Several methods have been proposed for this purpose. Some of them use empirical equations and geostatistical methods in order to minimize eventual errors due to interpolation. In this work a methodology is proposed for the development of 10΄ × 10΄ gridded isotopic data of precipitation in Central and Eastern Mediterranean. Statistical models are developed taking into account geographical and meteorological parameters as independent variables. The initial methodology takes into account only the altitude and latitude of an area. Since however the isotopic composition of precipitation depends also on longitude, the existing models have been modified by adding meteorological parameters as independent variables also. A series of models is proposed taking into account some or a combination of the above mentioned variables. The models are validated using the Thin Plate Smoothing Splines (TPSS) and the Ordinary Kriging (OK) methods.

Thesis (MSc (Geography and Environmental Studies))--University of Stellenbosch, 2007. / Due to the relative scarcity of weather stations, the climate conditions of large areas are not adequately represented by a weather station. This is especially true for regions with complex topographies or low population densities. Various interpolation techniques and software packages are available with which the climate of such areas can be calculated from surrounding weather stations’ data. This study investigates the possibility of using the software package ANUSPLIN to create accurate climate maps for the Western Cape, South Africa. ANUSPLIN makes use of thin plate smoothing splines and a digital elevation model to convert point data into grid format to represent an area’s climatic conditions. This software has been used successfully throughout the world, therefore a large body of literature is available on the topic, highlighting the limitations and successes of this interpolation method. Various factors have an effect on a region’s climate, the most influential being location (distance from the poles or equator), topography (height above sea level), distance from large water bodies, and other topographical factors such as slope and aspect. Until now latitude, longitude and the elevation of a weather station have most often been used as input variables to create climate grids, but the new version of ANUSPLIN (4.3) makes provision for additional variables. This study investigates the possibility of incorporating the effect of the surrounding oceans and topography (slope and aspect) in the interpolation process in order to create climate grids with a resolution of 90m x 90m. This is done for monthly mean daily maximum and minimum temperature and the mean monthly rainfall for the study area for each month of the year. Not many projects where additional variables have been incorporated in the interpolation process using ANUSPLIN are to be found in the literature, thus further investigation into the correct transformation and the units of these variables had to be done before they could be successfully incorporated. It was found that distance to oceans influences a region’s maximum and minimum temperatures, and to a lesser extent rainfall, while aspect and slope has an influence on a region’s rainfall. In order to assess the accuracy of the interpolation process, two methods were employed, namely statistical values produced during the spline function calculations by ANUSPLIN, and the removal of a selected number of stations in order to compare the interpolated values with the actual measured values. The analysis showed that more accurate maps were obtained when additional variables were incorporated into the interpolation process. Once the best transformations and units were identified for the additional variables, climate maps were produced in order to compare them with existing climate grids available for the study area. In general the temperatures were higher than those of the existing grids. For the rainfall grids ANUSPLIN’s produced higher rainfall values throughout the study region compared to the existing grids, except for the Southwestern Cape where the rainfall values were lower on north-facing slopes and high-lying area

Une prothèse de genou est généralement, composée de deux parties fixées respectivement sur le fémur et sur le tibia et d’une troisième, dite intercalaire. Durant le processus de fabrication de ces composants des déformations apparaissent au niveau des bruts de fonderie. Les fabricants de prothèses choisissent d’assurer l’épaisseur nominale de la prothèse en enlevant une épaisseur constante sur le brut de fonderie. Cette opération est généralement réalisée manuellement. L’objectif de ces travaux de thèse est de contribuer à l’automatisation de ces opérations en proposant une méthode d’adaptation des trajectoires d’usinage aux variations géométriques de la surface cible. L’objectif de ce travail de recherche est d’adapter une trajectoire d’usinage sur un modèle nominal pour enlever une épaisseur constante sur une surface brute de fonderie mesurée. La méthode proposée commence par une étape d’alignement de la surface mesurée sur la trajectoire nominale en utilisant un algorithme d’ICP. Par la suite, la trajectoire nominale est déformée pour venir enlever l'épaisseur désirée sur la surface brute mesurée. Cette dernière est définie, dans ces travaux, suivant un modèle STL. Naturellement, les discontinuités de ce type de modèle induit une impression des motifs du STL sur la trajectoire adaptée et, donc, sur la pièce usinée. Par la suite, afin de d’atténuer ce problème et d’améliorer la qualité de fabrication, il est proposé de procéder à un lissage de la trajectoire.Afin de valider les développements théoriques de ces travaux, des essais ont été réalisés sur une machine cinq axes pour l’ébauche de composants fémoraux d’une prothèse uni-compartimentale de genou. / Commonly, knee prostheses are composed of two parts fixed respectively on femur and tibia, and a third one called intercalary. During the manufacturing process, of these components distortions appear on roughcast workpiece geometry. Thus, prosthesis manufacturers choose to ensure the nominal thickness of the prosthesis by removing a constant thickness on the roughcast workpiece. This operation is generally carried out realized manually.The aim of this thesis is to contribute to the automation of these manual operations by providing a method to adapt the machining toolpaths at geometrical variations of the target surface. The aim of this research work is to adapt a machining toolpath computed on a nominal model to remove a constant thickness on a roughcast measured surface. The proposed method starts with an alignment step of the measured surface on the nominal toolpath using an ICP algorithm. Subsequently, the nominal toolpath is deformed to remove the desired thickness of the measured rough surface defined in presented case by a STL model. Naturally, discontinuities of this type of model induce the apparition of pattern for the STL on the adapted toolpath and thus on the machined workpiece. Subsequently, to limit this problem and to improve the quality of realized surface, it is proposed a toolpath smoothing method. To validate theoretical developments of this work, tests were carried out on a five-axis machine for roughing of femoral components of a unicompartmental knee prosthesis.

[pt] As alterações na legislação do Setor de Energia Elétrica Brasileiro em fins do milênio passado, provocou profundas mudanças no planejamento da Operação do Sistema e na Comercialização de energia elétrica no Brasil. O desmembramento das atividades de geração, de transmissão e de distribuição de energia elétrica criou novas características no comportamento dos Agentes Concessionários e as previsões de demanda por energia elétrica, que sempre foram ferramenta importante, por exemplo, na programação da operação, passaram a ser indispensáveis também, na comercialização de energia elétrica no mercado livre. Neste novo cenário, a obtenção e o armazenamento de dados confiáveis passou a ser parte integrante do patrimônio das Empresas e um sistema eficiente de previsões de carga passou a ser um diferencial na mesa de negociações. Os Agentes concessionários e o Operador Nacional do Sistema Elétrico vêm fazendo investimentos para aperfeiçoar os seus sistemas de aquisição de dados, entretanto em sistemas de multipontos algumas falhas imprevistas durante a sincronização da telemedição podem ocorrer, provocando defeitos nas séries. Nas séries de minuto em minuto, por exemplo, uma falha de algumas horas acarreta centenas de registros defeituosos e as principais publicações a respeito de modelagens de séries temporais para tratamento de dados não abordam as dificuldades encontradas diante de grandes falhas consecutivas nos dados. / [en] As a result of the continuing privatization process within the energy sector,electricity load forecasting is a ritical tool for decision-making in the Industry. Reliable forecasts are now needed not only for developing strategies for business planning and short term operational scheduling, but also to define the spot market electricity price. The forecasting process is data-ntensive and interest has been driven to shorter and shorter intervals. Large investments are being made in modernizing and improving metering systems, so as to make more data available to the forecaster. However, the forecaster is still faced with irregular time-series. Gaps, missing values, spurious information or repeated values in the time-series can result from transmission errors or small failures in the recording process. These so- called irregularities have led to research that focused on either iterative processes,like the Kalman filter and the EM algorithm, or applications of the statistical literature on treatment of missing values and outliers. Nevertheless, these methods often result in large forecast errors when confronted with consecutive failures in the data. On the other hand, the minute to minute series have a large amount of points and so the one day ahead forecast horizont becomes very large to handling with the conventional methods. In this context, we propose an alternative to detect and replace values and present a methodology to perform the forecasting process by using of other information in the time-series that relate to the variability and seasonality, which are commonly encountered in electricity load-forecasting data. We illustrate the method and address the problem as part of a wider project that aims at the development of an automatic on line system for tracking the Brazilian Interlinked Electric Network Operation and performing short term load forecasting. The data were collected by ONS / ELETROBRAS - Brazil. We concentrate on 10 minutes data for the years 1997-1999 of Light Serviços de Eletricidade S.A. (Rio de Janeiro and its surroundings). / [es] Las alteraciones en la legislación del Sector de Energía Elétrica Brasilero a finales del milenio pasado, provocó profundos cambios en el planificación de la Operación del Sistema y en la Comercialización de energía eléctrica en Brasil. La desarticulación de las actividades de generación, de transmisión y de distribuición de energía eléctrica creó nuevas características en el comportamiento de los Agentes Concesionarios. Así, las previsiones de demanda por energía eléctrica, que siempre fueron una herramienta importante, por ejemplo, en la programación de la operación, pasaron a ser indispensables también en la comercialización de energía eléctrica en el mercado libre. En este nuevo escenario, la obtención y almacenamiento de datos confiables pasó a ser parte integrante del patrimonio de las Empresas y un sistema eficiente de previsiones de carga constituye un diferencial en la mesa de negociaciones. Los Agentes concesionarios y el Operador Nacional del Sistema Eléctrico han invertido en el perfeccionamiento de sus sistemas de adquisición de datos. Sin embargo, en sistemas de multipuntos algunas fallas imprevistas durante la sincronización de la telemedición pueden ocurrir, provocando defectos en las series. En las series de minuto en minuto, por ejemplo, una falla de algunas horas trae consigo centenas de registros defectuosos y las principales publicaciones sobre modelos de series temporales para tratamiento de datos no abordan las dificuldades encontradas frente a grandes fallas consecutivas en los datos.

Given the importance of agricultural income for rural households, erratic weather conditions pose an austere threat to these households' livelihoods. This thesis explores ways through which households in agrarian economies smooth their consumption, engage in community networks, and readjust their labour allocation in response to shocks. In a setting of inherent risk, absence of institutional insurance, and labour market inefficiencies, poor households are often left to their own devices to cope with risk. The aim of this study is to examine the different risk-coping strategies adopted by households in rural India, assess their effectiveness, and derive implications for public policy. The results suggest that, in an environment characterised by agro-climatic risk, households are able to self-insure and smooth their consumption in the face of income shocks. Their coping mechanisms, however, may reduce their resilience to future shocks. In fact, small landholders tend to rely more heavily on their productive asset stock, while medium landholders find it optimal to preserve and accumulate their productive assets when exposed to exogenous income shocks. Households also change their labour allocation and reduce their self-employment in agriculture. Furthermore, households in rural areas can migrate to urban areas or engage in societal risk-sharing arrangements to mitigate the risk. The results of this thesis suggest that being part of a community network discourages individuals' migration and increases the likelihood of undertaking riskier activities. The findings also confirm the importance of portfolio adjustments and the diversification of household assets in buffering consumption. These conclusions form the basis of several policy implications, the most important of which is providing formal insurance schemes to encourage the accumulation of assets, technology, and skills.

Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity

[pt] A presente dissertação tem como principal objetivo a conceituação e apresentação das metodologias básicas de previsão de demanda e, a partir de um estudo de caso, a seleção da metodologia mais adequada e sua respectiva implantação. No primeiro capítulo é apresentada, além da importância do referido tema, a empresa selecionada para aplicação dos conceitos levantados, com a descrição de seus principais processos internos. No segundo capítulo foram abordados os conceitos de previsão de demanda e uma revisão dos principais modelos existentes. No capítulo seguinte, o problema que deverá ser tratado com a metodologia proposta é apresentado. Neste momento a metodologia conceituada é aplicada, através da seleção do método de previsão mais adequado ao caso estudado e respectiva modelagem, buscando melhorias em relação aos métodos de previsão existentes na empresa. Neste processo de modelagem utilizou-se o software Forecast Pro, um dos mais conceituados aplicativos de previsão de demanda no mercado. Por fim, na conclusão, avalia-se o impacto das mudanças propostas nos resultados da empresa, principalmente o aumento da precisão da previsão da demanda e, conseqüentemente, redução dos custos de importação e dos índices de stockout. / [en] The main objective of this dissertation is the presentation of basic forecasting methods and their implementation in a case study in supply chain. The first chapter points out the importance of forecasting in this context and describes the company selected for the case study and some of its internal processes that will be under scrutiny in the case study presented in this dissertation. The second chapter discusses the concepts and models of forecasting and reviews some of the major techniques in the field. In chapter three, standard forecasting techniques are apllied to real data (ten time series) from the company and select the most appropriate model in each case. Model adjustment is performed through the Forecast Pro software, one of the best-known products in the market. Chapter four contains the conclusions and the evaluation of the impacts of the proposed methodology on the company s results, especially the increased accuracy of forecasting and, consequently, the reduction in the import costs and stock out index.