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.

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.

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.

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.

Sample average approximation (SAA) is a well-known solution methodology for traditional stochastic programs which are risk neutral in the sense that they consider optimization of expectation functionals. In this thesis we establish sample average approximation methods for two classes of non-traditional stochastic programs. The first class is that of stochastic min-max programs, i.e., min-max problems with expected value objectives, and the second class is that of expected value constrained stochastic programs. We specialize these SAA methods for risk-averse stochastic problems with a bi-criteria objective involving mean and mean absolute deviation, and those with constraints on conditional value-at-risk. For the proposed SAA methods, we prove that the results of the SAA problem converge exponentially fast to their counterparts for the true problem as the sample size increases. We also propose implementation schemes which return not only candidate solutions but also statistical upper and lower bound estimates on the optimal value of the true problem. We apply the proposed methods to solve portfolio selection and supply chain network design problems. Our computational results reflect good performance of the proposed SAA schemes. We also investigate the effect of various types of risk-averse stochastic programming models in controlling risk in these problems.

In this study within quantitative portfolio optimization, stochastic programming is investigated as an investment decision tool. This research takes the direction of scenario based Mean-Absolute Deviation and is compared with the traditional Mean-Variance model and widely used Risk Parity portfolio. Furthermore, this thesis is done in collaboration with the First Swedish National Pension Fund, AP1, and the implemented multi-asset portfolios are thus tailored to match their investment style. The models are evaluated on two different fund management levels, in order to study if the portfolio performance benefits from a more restricted feasible domain. This research concludes that stochastic programming over the investigated time period is inferior to Risk Parity, but outperforms the Mean-Variance Model. The biggest aw of the model is its poor performance during periods of market stress. However, the model showed superior results during normal market conditions. / I denna studie inom kvantitativ portföljoptimering undersöks stokastisk programmering som ett investeringsbeslutsverktyg. Denna studie tar riktningen för scenariobaserad Mean-Absolute Deviation och jämförs med den traditionella Mean-Variance-modellen samt den utbrett använda Risk Parity-portföljen. Avhandlingen görs i samarbete med Första AP-fonden, och de implementerade portföljerna, med era tillgångsslag, är därför skräddarsydda för att matcha deras investeringsstil. Modellerna utvärderas på två olika fondhanteringsnivåer för att studera om portföljens prestanda drar nytta av en mer restrektiv optimeringsmodell. Den här undersökningen visar att stokastisk programmering under undersökta tidsperioder presterar något sämre än Risk Parity, men överträffar Mean-Variance. Modellens största brist är dess prestanda under perioder av marknadsstress. Modellen visade dock något bättre resultat under normala marknadsförhållanden.

Wilcox (1990) examined the Type I and Type II error rates for several robust tests of H0: σ12/σ22 = 1 in paired-data designs and concluded that a satisfactory solution does not yet exist. A confidence interval for a ratio of correlated mean absolute deviations is derived and performs well in small sample sizes across realistically nonnormal distributions. When used to test a hypothesis, the proposed confidence interval is almost as powerful as the most powerful test examined by Wilcox.