Master of Science / Department of Statistics / Gary Gadbury / This report illustrates how to use two statistic methods to investigate the performance of a new technique to detect breast cancer and lung cancer at early stages. The two methods include logistic regression and classification and regression tree (CART). It is found that the technique is effective in detecting breast cancer and lung cancer, with both sensitivity and specificity close to 0.9. But the ability of this technique to predict the actual stages of cancer is low. The age variable improves the ability of logistic regression in predicting the existence of breast cancer for the samples used in this report. But since the sample sizes are small, it is impossible to conclude that including the age variable helps the prediction of breast cancer. Including the age variable does not improve the ability to predict the existence of lung cancer. If the age variable is excluded, CART and logistic regression give a very close result.

Master of Science / Statistics / Weixing Song / In this report, an improved estimation procedure for the regression parameter in simple linear regression models with the Laplace measurement error is proposed. The estimation procedure is made feasible by a Tweedie type equality established for E(X|Z), where Z = X + U, X and U are independent, and U follows a Laplace distribution. When the density function of X is unknown, a kernel estimator for E(X|Z) is constructed in the estimation procedure. A leave-one-out cross validation bandwidth selection method is designed. The finite sample performance of the proposed estimation procedure is evaluated by simulation studies. Comparison study is also conducted to show the superiority of the proposed estimation procedure over some existing estimation methods.

Regression testing is essential to ensure software quality. Regression Test-case selection is another process wherein, the testers would like to ensure that test-cases which are obsolete due to the changes in the system should not be considered for further testing. This is the Regression Test-case Selection problem. Although existing research has addressed many related problems, most of the existing regression test-case selection techniques cater to procedural systems. Being academic, they lack the scalability and detail to cater to multi-tier applications. Such techniques can be employed for procedural systems, usually mathematical applications. Enterprise applications have become complex and distributed leading to component-based architectures. Thus, inter-process communication has become a very important activity of any such system. Messaging is the most widely employed intermodule interaction mechanism. Today's systems, being heavily internet dependent, are Web-Services based which utilize XML for messaging. We propose an RTS technique which is specifically targeted at enterprise applications.

Det klassiska transportproblemet är ett linjärt och kontinuerligt optimeringsproblem vilket vanligtvis kan lösas till optimalitet snabbt och effektivt med t.ex. simplex-metoden. Men väldigt stora instanser (> 10 000 000 variabler) är minneskrävande och tar lång tid att lösa även för state-of-the-art lösare.Syftet med undersökningen är att hitta ett eller flera sätt att skatta det optimala målfunktionsvärdet för transportproblemet utan att lösa problemet. Olika nyckeltal och karakteristika för probleminstanser till transportproblemet har tagits fram, och dessa har sedan använts för att ta fram linjära regressionsmodeller. För att få en helhetsbild av hur funktionerna och nyckeltalen fungerar på transportproblemet skapas ett antal extremfall. Dessa extremfall är olika sätt att placera ut noder. Resultatet visar att linjär regression inte är tillräckligt för att lösa problemet i samtliga fall. Vi ser dock att det är möjligt att hitta bra skattningar till det optimala målfuntionsvärdet i vissa specialfall. / The classical transportation problem is a linear and continous optimization problem which can usually be solved quickly and easily with for example the simplex method. However, larger instances of the problem (> 10 000 000 variables) requires a lot of memory and takes a long time to solve, even for state-of-the-art solvers. The purpose of this investigation is to find one or more ways to estimate the optimal objective value for the transportation problem without solving it. Different key values and characteristics for the transportation problem have been investigated and these values have then been used to derive linear regression models. In order to get the big picture of how the functions and key values work on the transportation problem, a set of extreme cases is created. These extreme cases are different ways to place nodes. The results show that linear regression is not enough to solve the problem in all cases. However, under certain circumstances we see that it is possible to find good estimates to optimal objective value.

Neste trabalho estudamos modelos lineares de regressão para a análise de dados obtidos de pesquisas amostrais complexas. Foram considerados aspectos teóricos e aplicações a conjuntos de dados reais por meio do uso do aplicativo SUDAAN e da biblioteca ADAC da linguagem R. Nas aplicações foram abordados os modelos de regressão normal e logística. Foram realizados também estudos comparativos dos métodos estudados com os que assumem que as observações são selecionadas segundo amostragem aleatória simples. / We have studied linear regression models for data analysis when the data set comes from a complex sampling survey. We have considered theoretical aspects and some applications utilizing the SUDAAN software and the ADAC library for R language. The applications involved the normal and logistic regression models. The studied methods were compared with those obtained from simple random samples.

Thesis advisor: Zhijie Xiao / My dissertation research examines empirical issues in financial economics with a special focus on the application of quantile regression. This dissertation is composed by two self-contained papers, which center around: (1) robust estimation of conditional idiosyncratic volatility of asset returns to offer better understanding of market microstructure and asset pricing anomalies; (2) implementation of coherent risk measures in portfolio selection and financial risk management. The first chapter analyzes the roles of idiosyncratic risk and firm-level conditional skewness in determining cross-sectional returns. It is shown that the traditional EGARCH estimates of conditional idiosyncratic volatility may bring significant finite sample estimation errors in the presence of non-Gaussianity, casting strong doubt on the positive intertemporal idiosyncratic volatility effect reported in the literature. We propose an alternative estimator for conditional idiosyncratic volatility for GARCH-type models. The proposed estimation method does not require error distribution assumptions and is robust non-Gaussian innovations. Monte Carlo evidence indicates that the proposed estimator has much improved sampling performance over the EGARCH MLE in the presence of heavy-tail or skewed innovations. Our cross-section portfolio analysis demonstrates that the idiosyncratic volatility puzzle documented by Ang, Hodrick, Xiang and Zhang (2006) exists intertemporally, i.e., stocks with high conditional idiosyncratic volatility earn abnormally low returns. We solve the major piece of this puzzle by pointing out that previous empirical studies have failed to consider both idiosyncratic variance and individual conditional skewness in determining cross-sectional returns. We introduce a new concept - the "expected windfall" - as an alternative measure of conditional return skewness. After controlling for these two additional factors, cross-sectional regression tests identify a positive relationship between conditional idiosyncratic volatility and expected returns for over 99% of the total market capitalization of the NYSE, NASDAQ, and AMEX stock exchanges. The second chapter examines portfolio allocation decision for investors with general pessimistic preferences (GPP) regarding downside risk aversion and out-performing benchmark returns. I show that the expected utility of pessimistic investors can be robustly estimated within a quantile regression framework without assuming asset return distributions. The asymptotic properties of the optimal portfolio weights are derived. Empirically, this method is introduced to construct the optimal fund of CSFB/Tremont hedge-fund indices. Both the in-sample and out-of-sample backtesting results confirm that the optimal mean-GPP portfolio outperforms the mean-variance and mean-conditional VaR portfolios. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

by Chung Sai Ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 53-56). / SUMMARY / Chapter 1. --- Introduction --- p.1 / "Functional, Structural and Ultrastructural Relationships" --- p.2 / Identifiability --- p.4 / Non-normally Distributed Regressor --- p.5 / Chapter 2. --- Underlying Non-normality --- p.7 / Beta Regressor and Guassian Errors --- p.8 / Moments --- p.14 / Moment Generating Function & Characteristic Function --- p.17 / Modality --- p.18 / Distribution Portfolio --- p.21 / Chapter 3. --- Modified Maximum Likelihood Estimation --- p.24 / Consistency --- p.26 / Asymptotically Normality --- p.30 / Efficiency of the MMLE --- p.34 / Chapter 4. --- Monte Carlo Simulation Studies --- p.36 / The Use of MMLE --- p.36 / Third Order Moment Estimator with Asymptotically Minimal Variance --- p.42 / Robustness --- p.46 / Chapter 5. --- Discussions and Conclusions --- p.48 / Other Alternatives --- p.48 / Semiparametric and Nonparametric Maximum Likelihood Estimation --- p.51 / References --- p.53

by Koon-Sun Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 40-41). / Chapter Chapter 1 --- Introduction and Review --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Preliminaries --- p.4 / Chapter 1.3 --- A brief review of A-optimal designs --- p.8 / Chapter Chapter 2 --- D-optimal Designs --- p.13 / Chapter 2.1 --- A D-optimal design problem --- p.13 / Chapter 2.2 --- A theorem for D-optimal designs --- p.14 / Chapter Chapter 3 --- E-optimal Designs --- p.18 / Chapter 3.1 --- An E-optimal design problem --- p.18 / Chapter 3.2 --- A theorem for E-optimal designs --- p.19 / Chapter Chapter 4 --- An alternative method for computing CL vectors --- p.31 / Chapter Chapter 5 --- Conclusions --- p.36 / References --- p.40

Chan Wing-Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 43-45). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Estimation of Volatility --- p.5 / Chapter 2.1 --- A revisit to the RiskMetrics --- p.6 / Chapter 2.2 --- Predicting Multiple-period of Volatilities --- p.7 / Chapter 2.3 --- Performance Measures --- p.11 / Chapter 2.4 --- Nonparametric Estimation of Quantiles --- p.13 / Chapter 3 --- Univariate Prediction --- p.15 / Chapter 3.1 --- Piecewise Constant Technique --- p.16 / Chapter 3.2 --- Piecewise Linear Technique --- p.22 / Chapter 4 --- Bivariate Prediction --- p.27 / Chapter 4.1 --- Model Selection --- p.28 / Chapter 4.2 --- Piecewise Linear with Discontinuity --- p.29 / Chapter 4.3 --- Piecewise Linear Technique --- p.35 / Chapter 5 --- Conclusions --- p.41 / Bibliography --- p.43

by Chun-Wai Sit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 91-92). / Abstract also in Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Ridge Regression --- p.3 / Chapter 1.2 --- Generalized Ridge Regression and Present Work --- p.11 / Chapter Chapter 2 --- Shrinkage Estimation of Regression Coefficients --- p.14 / Chapter 2.1 --- Introduction --- p.15 / Chapter 2.2 --- Dominance over the Least Squares Estimator --- p.17 / Chapter 2.3 --- Dominance over the Ridge Estimator --- p.26 / Chapter 2.4 --- Bayesian Motivation --- p.31 / Chapter 2.5 --- Choosing the Shrinkage Factor --- p.33 / Chapter 2.5.1 --- Generalized Cross-Validation (GCV) --- p.34 / Chapter 2.5.2 --- RIDGM --- p.35 / Chapter 2.5.3 --- Iterative method for selecting the optimum parameter (IA) --- p.38 / Chapter 2.5.4 --- Empirical Bayes Approach --- p.45 / Chapter Chapter 3 --- Simulation Study --- p.47 / Chapter 3.1 --- Simulation Plan --- p.48 / Chapter 3.2 --- Simulation Result --- p.54 / Chapter 3.2.1 --- β = βL --- p.55 / Chapter 3.2.2 --- β = βs --- p.61 / Chapter 3.3 --- Average k and a --- p.67 / Chapter 3.3.1 --- Shrinkage Estimator --- p.67 / Chapter 3.3.2 --- Ridge Estimator --- p.78 / Chapter 3.4 --- Conclusion --- p.88 / References --- p.91