This paper is concerned with the problem of computing theapproximate D-optimal design for polynomial regression with weight function w(x)>0 on the design interval I=[m_0-a,m_0+a]. It is shown that if w'(x)/w(x) is a rational function on I and a is close to zero, then the problem of constructing D-optimal designs can be transformed into a differential equation problem leading us to a certain matrix including a finite number of auxiliary unknown constants, which can be approximated by a Taylor expansion. We provide a recursive algorithm to compute Taylor expansion of these constants. Moreover, the D-optimal interior support points are the zeros of a polynomial which has coefficients that can be computed from a linear system.

This paper is concerned with the problem of constructing A-optimal design for polynomial regression with analytic weight function on the interval [m-a,m+a]. It is shown that the structure of the optimal design depends on a and weight function only, as a close to 0. Moreover, if the weight function is an analytic function a, then a scaled version of optimal support points and weights is analytic functions of a at $a=0$. We make use of a Taylor expansion which coefficients can be determined recursively, for calculating the A-optimal designs.

This paper is devoted to studying the problem of constructing Ds-optimal design for d-th degree polynomial regression with analytic weight function on the interval [m-a,m+a],m,a in R. It is demonstrated that the structure of the optimal design depends on d, a and weight function only, as a close to 0. Moreover, the Taylor polynomials of the scaled versions of the optimal support points and weights can be computed via a recursive formula.

The problem in this thesis was originally motivated by problems presented with documents of Early England Data Set (DEEDS). The central problem with these medieval documents is the lack of methods to assign accurate dates to those documents which bear no date. With the problems of the DEEDS documents in mind, we present two methods to impute missing features of texts. In the first method, we suggest a new class of metrics for measuring distances between texts. We then show how to combine the distances between the texts using statistical smoothing. This method can be adapted to settings where the features of the texts are ordered or unordered categoricals (as in the case of, for example, authorship assignment problems). In the second method, we estimate the probability of occurrences of words in texts using nonparametric regression techniques of local polynomial fitting with kernel weight to generalized linear models. We combine the estimated probability of occurrences of words of a text to estimate the probability of occurrence of a text as a function of its feature -- the feature in this case being the date in which the text is written. The application and results of our methods to the DEEDS documents are presented.

A estimação e previsão da volatilidade de ativos são de suma importância para os mercados financeiros. Temas como risco e incerteza na teoria econômica moderna incentivaram a procura por métodos capazes de modelar uma variância condicional que evolui ao longo do tempo. O objetivo principal desta dissertação é comparar alguns métodos de regressão global e local quanto à extração da volatilidade dos índices Ibovespa e Standard and Poor´s 500. Para isto, são realizadas estimações e previsões com os modelos GARCH paramétricos e com os modelos aditivos semi-paramétricos. Os primeiros, tradicionalmente utilizados na estimação de segundos momentos condicionais, têm sua capacidade sugerida em diversos artigos. Os segundos provêm alta flexibilidade e descrições visualmente informativas das relações entre as variáveis, tais como assimetrias e não linearidades. Sendo assim, testar o desempenho dos últimos frente às estruturas paramétricas consagradas apresenta-se como uma investigação apropriada. A realização das comparações ocorre em períodos selecionados de alta volatilidade no mercado financeiro internacional (crises), sendo a performance dos modelos medida dentro e fora da amostra. Os resultados encontrados sugerem a capacidade dos modelos semi-paramétricos em estimar e prever a volatilidade dos retornos dos índices nos momentos analisados. / Volatility estimation and forecasting are very important matters for the financial markets. Themes like risk and uncertainty in modern economic theory have encouraged the search for methods that allow for the modeling of time varying variances. The main objective of this dissertation is to compare global and local regressions in terms of their capacity to extract the volatility of Ibovespa and Standard and Poor 500 indexes. To achieve this aim, parametric GARCH and semiparametric additive models estimation and forecasting are performed. The first ones, traditionally applied in the estimation of conditional second moments, have their capacity suggested in many papers. The second ones provide high flexibility and visually informative descriptions of the relationships between the variables, like asymmetries and nonlinearities. Therefore, testing the last ones´ performance against the acknowledged parametric structures is an appropriate investigation. Comparisons are made in selected periods of high volatility in the international financial market (crisis), measuring the models´ performance inside and outside sample. The results that were found suggest the capacity of semiparametric models to estimate and forecast the Indexes returns´ volatility at the analyzed moments.

The aim of this thesis is to provide an overview of the varying coefficient mod- els - a class of regression models that allow the coefficients to vary as functions of random variables. This concept is described for independent samples, longi- tudinal data, and time series. Estimation methods include polynomial spline, smoothing spline, and local polynomial methods for models of a linear form and local maximum likelihood method for models of a generalized linear form. The statistical properties focus on the consistency and asymptotical distribution of the estimators. The numerical study compares the finite sample performance of the estimators of coefficient functions. 1

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This thesis studies regression discontinuity designs with the use of additional covariates for estimation of the average treatment effect. We prove asymptotic normality of the covariate-adjusted estimator under sufficient regularity conditions. In the case of a high-dimensional setting with a large number of covariates depending on the number of observations, we discuss a Lasso-based selection approach as well as alternatives based on calculated correlation thresholds. We present simulation results on those alternative selection strategies.:1. Introduction 2. Preliminaries 3. Regression Discontinuity Designs 4. Setup and Notation 5. Computing the Bias 6. Asymptotic Behavior 7. Asymptotic Normality of the Estimator 8. Including Potentially Many Covariates 9. Simulations 10. Conclusion

In recent years more companies have invested in electronic commerce as a result of more customers using the internet as a tool for shopping. However, the basics of marketing still apply to online stores, and thus companies need to conduct market analyses of customers and the online market to be able to successfully target customers online. In this report, we propose the use of machine learning, a tool that has received a lot of attention and positive affirmation for the ability to tackle a range of problems, to predict future trends of electronic commerce in Sweden. More precise, to predict the future share of users of electronic commerce in general and for certain demographics. We will build three different models, polynomial regression, SVR and ARIMA. The findings from the constructed forecasts were that there are differences between different demographics of customers and between groups within a certain demographic. Furthermore, the result showed that the forecast was more accurate when modelling a certain demographic than the entire population. Companies can thereby possibly use the models to predict the behaviour of certain smaller segments of the market and use that in their marketing to attract these customers. / Pa senare år har många företag investerat i elektronisk handel, även kallat e-handel, vilket är ett resultat av att individer i samhället i större utsträckning använder internet som ett redskap. Grunderna för marknadsföring gäller fortfarande för webbaserade butiker, och därmed behöver företag genomföra marknadsanalyser över potentiella kunder och internet-marknaden för att kunna lansera starka marknadsföringskampanjer. I denna rapport föreslår vi användning av maskininlärning, ett verktyg som har fått mycket uppmärksamhet på senaste tiden för dess förmåga att hantera olika problem kring data och för att prognostisera framtida trender för e-handel i Sverige. Mer exakt kommer andelen användare av e-handel i framtiden prognostiseras, både generellt och för enskilda demografier. Vi kommer att implementera tre olika modeller, polynomisk regression, SVR och ARIMA. Resultaten från de konstruerade prognoserna visar att det finns tydliga skillnader mellan olika demografier av kunder och mellan grupper inom en viss demografi. Dessutom visade resultaten att prognoserna var mer exakta vid modellering av en viss demografi än över hela befolkningen. Företag kan därmed möjligtvis använda modellerna för att förutsäga beteendet hos vissa mindre segment av marknaden.

This thesis studies a DC motor for a racing hybrid electric vehicle (HEV) prototype.The development of optimization-based energy management strategies (EMS) necessitates an accurate quasi-static model of the driving motor, which includes a 2D efficiency map with the torque outputand rotating speed as the inputs. However, a DC motor's efficiency varies a lot at differentoperating points and the efficiency map from the technical manual does not match the various applications in reality.In view of this, this thesis investigates a field testing based quasi-static modeling method to construct the DC motor efficiency map with only portable and brief testing resources. Firstly, a testbench is designed, manufactured, integrated, and configured with necessary accessories. The testbench consists of the motor under test, a braking motor to provide load torque, a servo-amplifier for torque control and sensing, a host computer for data acquisition, and power supplies. Then, a self-contained testing plan is designed by which as many as possible different testing points can be covered based on the braking motor's power limit. After that, the experiments are successively performed on the test bench, and the input electric power along with the output mechanical power at steady state are recorded. Multiple data process methods are explored to analyze the collected testing data. Root mean square (RMS) is used to reduce the measuring variance. Invalid outliers are identified and filtered out based on the residuals. The qualified samples are employed to build up the 2D efficiency map by fourth-degree polynomial regression. Then, three methods, linear, quadratic, and cubic fittings are attempted separately to estimate the relationships between the input power and output torque at different speeds. The results show that the quadratic model is the best option which results in smaller root mean square error (RMSE) and fair computation complexity. To conclude, the quasi-static dynamic model of a DC motor, which includes a 2D efficiency map and the speed-based polynomial expression of input power, can be properly established by a new method relying on less and simpler devices in contrast to those traditional methods. This method bypasses a bulk of tedious modulations on precise motor speed control which is heavily dependent on a high-precision sensor. The formulated 2D efficiency map will effectively support the future development of model-based EMS. The polynomial expression provides a more efficient approach to estimate instantaneous energy efficiency for an embedded system application. / Denna avhandling studerar en likströmsmotor för en prototyp av ett elektriskt hybridfordon (HEV) för racing. Utvecklingen av optimeringsbaserade energihanteringsstrategier (EMS) kräver en precis kvasistatisk dynamisk modell av den drivande motorn, som inkluderar en en 2D-karta (effektivetetskarta) som beskriver hur verkningsgraden beror på moment och rotationshastighet. Verkningsgraden hos likströmsmotorn varierar dock mycket beroende på arbetspunkt och verkningsgradskartan från databladen stämmer inte alltid med de olika applikationerna i verkligheten. Givet detta undersöker denna avhandling en fältprovsbaserad kvasistatisk modelleringsmetod för att uppskatta likströmsmotorns effektivitetskarta med endast flyttbara och begränsade testresurser. Till att börja med är en testbänk designad, tillverkad, integrerad och konfigurerad med alla nödvändiga komponenter. Testbänken består av den motor som testas, en bromsmotor för att ge belastningsmoment, en servoförstärkare för vridmomentstyrning och mätning, samt en dator för datainsamling och strömförsörjning. Sedan utformas en fristående testplan som gör att så många olika testpunkter som möjligt kan täckas, baserat på bromsmotorn effektgräns. Därefter utförs experimenten successivt på testbänken där ingående elektrisk effekt och utgående mekanisk effekt mäts i jämviktsläget. Flera olika metoder undersöks för att analysera den insamlade testdatan. Kvadratiskt medelvärde används för att minska variansen i testdatan. Ogiltiga outliers identifieras och filtreras ut baserat på hur mycket de avviker från medelvärdet. De godkända testpunkterna används för att bygga upp 2D-effektivitetskartan genom en fjärde gradens polynom regression. Därefter används tre olika metoder, linjära, kvadratiska och kubiska för att skapa kurvanpassningar genom polynomregression för att beskriva sambandet mellan ingångseffekt och utgångseffekt vid olika hastigheter. Resultaten visar att den kvadratiska metoden är det bästa alternativet eftersom det ger en mindre medelkvadratavvikelse och en hanterbar beräkningskomplexitet. Avslutningsvis kan den kvasistatiska dynamiska modellen för en likströmsmotor, som inkluderar en 2D-effektivitetskarta med det hastighetsbaserade polynomuttrycket för ingångseffekt, skapas av en ny metod som förliter sig på mindre och enklare materiel än traditionella metoder. Denna metod kringår en stor del av den omständiga modulering som precis varvtalsstyrning kräver vilken även är väldigt beroende på högprecisionssensorer. Den formulerade 2D-effektivitetskartan kommer ge betydande stöd till framtida utveckling av modelbaserade energihanteringsstrategier 2 (EMS). Polynomuttrycket ger ett mer effektivt tillvägagångssätt för att uppskatta omedelbar energieffektivitet för en inbäddad systemapplikation.