A plot that includes multiple location and spread statistics can provide useful information about the shape of a distribution, not only with respect to location and variability but also with respect to skewness and kurtosis. We propose a plot containing the interquartile range, mean absolute deviation, standard deviation, and range of a dataset. The comparison of the spread statistics gives information about kurtosis and the comparison of the location statistics gives information about skewness. After the distribution has been divided into two parts by the median, the interquartile range can be thought of as the distance between the medians in each half of the distribution. We explain how the mean absolute deviation with respect to the median can similarly be visualized as half the distance between the means in each half of the distribution. An R function to produce the polyplot is available as an online supplement.

A new confidence interval for the coefficient of dispersion (mean absolute deviation from the median divided by median) is proposed and is shown to perform better than the BCa bootstrap confidence interval.

This thesis is an implementation project of a portfolio optimization model, with the purpose of creating a decision support tool. It aims to provide quantitative input to the portfolio construction process at Handelsbanken Fonder, by applying Konno & Yamazaki’s Mean Absolute Deviation method, with a Feinstein & Thapa modification. Additionally, the Black-Litterman model is implemented to approximate the input of expected return. The linear optimization problem was then solved by the Simplex algorithm. The main deliverable is a model that can assist portfolio managers in making investment decisions. Back-testing of the model showed that it did not outperform the benchmark portfolios, which is likely a result of only allowing long positions in the model. Nevertheless, the model provides value by giving the user a second opinion on the efficient frontier, for any given investment decision. / Den här uppsatsen är ettimplementationsprojekt av enportföljoptimerings-modell, med syftet att skapaett beslutsstödjande verktyg. Den strävar efter att ge ett kvantitativt bidragtill portföljallokerings-processen på Handelsbanken Fonder, genom att användaKonno & Yamazaki’s Mean Absolute Deviation-metod med en Feinstein &Thapa-modifiering. Vidare har Black-Littermanmodellen implementerats för attapproximera den förväntade avkastningen. Det linjära optimeringsproblemetlöstes sedan med Simplex-algorithmen. Det huvudsakliga resultatet är en modellsom kan assisterafondförvaltare i investeringsbeslut. Utförda utfallstestvisade att modellen inte överträffade de använda benchmark-fonderna, vilketsannolikt är ett resultat av att modellen enbart tillåterlånga positioner.Likväl, kan modellen vara värdefull genom att erbjuda användaren ett alternativpå den effektiva fronten, för ett givet investeringsbeslut.

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.

No description available.

In this thesis, we study how sovereign credit default swaps are able to measure systemic risk as well as how they can be used to construct optimal portfolios to minimize risk. We define the clustering coefficient as a proxy for systemic risk and design an optimization problem with the goal of minimizing the mean absolute deviation of the clustering coefficient on a group of nine European countries. Additionally, we define a metric we call the diversity score that measures the diversification of any given portfolio. We solve this problem for a baseline set of parameters, then spend the remainder of the thesis modifying these parameters to investigate how the optimal solution and diversity score are impacted.

Eccentric lunar frozen orbits are analyzed in this study in relation to lunar navigation and communications missions, particularly the proposed Magnolia-1 mission. An overview of the Earth/Moon system, frozen orbits, and the Magnolia-1 mission is provided. A review of existing literature is presented, and potential limitations are discussed. Both preliminary and numerical perturbation analyses are presented, and a general set of perturbations for further analysis of high-altitude lunar orbits is identified. Analysis of potential orbits for the Magnolia-1 mission is performed through calculation of a maximum deviation metric and through visualization as a function of initial orbital elements. Trends are identified within a closed search space by varying elements individually and in combination. Potential orbit designs for the Magnolia-1 mission are selected and compared to established alternatives. A method of orbit refinement is used to improve behavior, and coverage and eclipse analyses are performed to establish suitability. Conclusions are made involving general trends related to eccentric lunar frozen orbits and the specific designs proposed for the Magnolia-1 mission, and a method for the design of similar orbits is suggested. Ideas for further study are also presented.

In the thesis, the Wilcoxon approach to linear regression problems is combined with the fractal image compression to form a novel Wilcoxon fractal image compression. When the original image is corrupted by noise, we argue that the fractal image compression scheme should be insensitive to those outliers present in the corrupted image. This leads to the new concept of robust fractal image compression. The proposed Wilcoxon fractal image compression is the first attempt toward the design of robust fractal image compression. Four different numerical methods, i.e., steepest decent, line minimization based on quadratic interpolation, line minimization based on cubic interpolation, and least absolute deviation, will be proposed to solve the associated linear Wilcoxon regression problem. From the simulation results, it will be seen that, compared with the traditional fractal image compression, Wilcoxon fractal image compression has very good robustness against outliers caused by salt-and-pepper noise. However, it does not show great improvement of the robustness against outliers caused by Gaussian noise.

In view of the current situation of fluctuating high crude oil prices, it is now more important than ever for petroleum refineries to operate at an optimal level in the present dynamic global economy. Acknowledging the shortcomings of deterministic models, this work proposes a hybrid of stochastic programming formulations for an optimal midterm refinery planning that addresses three factors of uncertainties, namely price of crude oil and saleable products, product demand, and production yields. An explicit stochastic programming technique is utilized by employing compensating slack variables to account for violations of constraints in order to increase model tractability. Four approaches are considered to ensure both solution and model robustness: (1) the Markowitz???s mean???variance (MV) model to handle randomness in the objective coefficients of prices by minimizing variance of the expected value of the random coefficients; (2) the two-stage stochastic programming with fixed recourse approach via scenario analysis to model randomness in the right-hand side and left-hand side coefficients by minimizing the expected recourse penalty costs due to constraints??? violations; (3) incorporation of the MV model within the framework developed in Approach 2 to minimize both the expectation and variance of the recourse costs; and (4) reformulation of the model in Approach 3 by adopting mean-absolute deviation (MAD) as the risk metric imposed by the recourse costs for a novel application to the petroleum refining industry. A representative numerical example is illustrated with the resulting outcome of higher net profits and increased robustness in solutions proposed by the stochastic models.

In questa tesi descriviamo una procedura automatizzata per l’analisi della corteccia motoria dello scimpanzè, del Macaca fascicularis e del cavallo, basata su un nuovo metodo computerizzato di analisi delle sezioni colorate attraverso il metodo di Nissl, al fine di studiare la corteccia cerebrale in specie differenti. Le microfotografie delle sezioni sono state elaborate con una procedura standardizzata usando il software ImageJ. Questa procedura ha previsto la suddivisione degli strati corticali, dal primo al sesto, in diversi frames. Per misurare la complessità delle cellule nervose (cioè quanto una cellula fosse diversa dalle adiacenti) abbiamo utilizzato un modello di rappresentazione statistica non-parametrica che mostra come la complessità può essere espressa in termini di un adeguato indice di dispersione statistica quale il MAD (mean absolute deviation). Abbiamo quindi dimostrato che gli strati piramidali della corteccia motoria del cavallo sono più irregolari di quelli di scimpanzè e Macaca fascicularis. La combinazione dell’analisi automatica delle immagini e delle analisi statistiche consente pertanto di confrontare e classificare la complessità della corteccia motoria attraverso diverse specie. Il modello viene proposto come strumento al fine di contribuire a stabilire le somiglianze cerebrali tra umani e animali, rispettando il principio delle 3R. / In this thesis we describe an automated procedure based on a new computerized method of partitioning Nissl-stained sections of the motor cortex of the chimpanzee, crab-eating monkey, and horse, to study the neocortex in different species. Microphotographs of the sections were first processed using a standard procedure in ImageJ, then the stained neuronal profiles were analyzed within continuously adjoining frames from the first to the sixth layer of neocortex. To measure the neuronal complexity (how a given cell is different from its neighbors) we used a general non-parametric data representation model showing that the complexity can be expressed in terms of a suitable measure of statistical dispersion such as the mean absolute deviation. We demonstrated that the pyramidal layers of the motor cortex of the horse are more irregular than those of the monkeys studied. The combination of automated image analysis and statistical analysis made it possible to compare and rank the motor cortex complexity across different species. Therefore, we are confident that our work will help to establish brain similarities between humans and animals used for alimentary purpose, whose brain is often discarded. This, in turn, will allow to carry out the experimental brain research obeying the 3Rs principle.