Thesis (Ph. D.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 343-360).

Thesis (Ph.D.)--University of Southern California, 2007. / Adviser: Ronald C. Henry. Includes bibliographical references.

Electricity is one of the most stolen commodities in the world. Electricity theft can be defined as the criminal act of stealing electrical power. Several types of electricity theft exist, including illegal connections and bypassing and tampering with energy meters. The negative financial impacts, due to lost revenue, of electricity theft are far reaching and affect both developing and developed countries. . Here in South Africa, Eskom loses over R2 Billion annually due to electricity theft. Data mining and nonparametric statistical methods have been used to detect fraudulent usage of electricity by assessing abnormalities and abrupt changes in kilowatt hour (kWh) consumption patterns. Identifying effective measures to detect fraudulent electricity usage is an active area of research in the electrical domain. In this study, Support Vector Machines (SVM), Naïve Bayes (NB) and k-Nearest Neighbour (KNN) algorithms were used to design and propose an electricity fraud detection model. Using the Nelson Mandela Bay Municipality as a case study, three classifiers were built with SVM, NB and KNN algorithms. The performance of these classifiers were evaluated and compared.

Kernel embedding methods have witnessed a great deal of practical success in the area of nonparametric hypothesis testing in recent years. But ever since its first proposal, there exists an inevitable problem that researchers in this area have been trying to answer--what kernel should be selected, because the performance of the associated nonparametric tests can vary dramatically with different kernels. While the way of kernel selection is usually ad hoc, we wonder if there exists a principled way of kernel selection so as to ensure that the associated nonparametric tests have good performance. As consistency results against fixed alternatives do not tell the full story about the power of the associated tests, we study their statistical performance within the minimax framework. First, focusing on the case of goodness-of-fit tests, our analyses show that a vanilla version of the kernel embedding based test could be suboptimal, and suggest a simple remedy by moderating the kernel. We prove that the moderated approach provides optimal tests for a wide range of deviations from the null and can also be made adaptive over a large collection of interpolation spaces. Then, we study the asymptotic properties of goodness-of-fit, homogeneity and independence tests using Gaussian kernels, arguably the most popular and successful among such tests. Our results provide theoretical justifications for this common practice by showing that tests using a Gaussian kernel with an appropriately chosen scaling parameter are minimax optimal against smooth alternatives in all three settings. In addition, our analysis also pinpoints the importance of choosing a diverging scaling parameter when using Gaussian kernels and suggests a data-driven choice of the scaling parameter that yields tests optimal, up to an iterated logarithmic factor, over a wide range of smooth alternatives. Numerical experiments are presented to further demonstrate the practical merits of our methodology.

My dissertation explores two broad areas in econometrics and statistics. The first area is nonparametric identification and estimation with endogeneity using instrumental variables. The second area is related to low-rank matrix recovery and high-dimensional panel data models. The following three chapters study different topics in these areas. Chapter 1 considers identification and estimation of triangular models with a discrete endogenous variable and an instrumental variable (IV) taking on fewer values. Using standard approaches, the small support set of the IV leads to under-identification due to the failure of the order condition. This chapter develops the first approach to restore identification for both separable and nonseparable models in this case by supplementing the IV with covariates, allowed to enter the model in an arbitrary way. For the separable model, I show that it satisfies a system of linear equations, yielding a simple identification condition and a closed-form estimator. For the nonseparable model, I develop a new identification argument by exploiting its continuity and monotonicity, leading to weak sufficient conditions for global identification. Built on it, I propose a uniformly consistent and asymptotically normal sieve estimator. I apply my approach to an empirical application of the return to education with a binary IV. Though under-identified by the IV alone, I obtain results consistent with the empirical literature using my method. I also illustrate the applicability of the approach via an application of preschool program selection where the supplementation procedure fails. Chapter 2, written with Jushan Bai, studies low-rank matrix recovery with a non-sparse error matrix. Sparsity or approximate sparsity is often imposed on the error matrix for low-rank matrix recovery in statistics and machine learning literature. In econometrics, on the other hand, it is more common to impose a location normalization for the stochastic errors. This chapter sheds light on the deep connection between the median zero assumption and the sparsity-type assumptions by showing that the principal component pursuit method, a popular approach for low-rank matrix recovery by Candès et al. (2011), consistently estimates the low-rank component under a median zero assumption. The proof relies on a new theoretical argument showing that the median-zero error matrix can be decomposed into a matrix with a sufficient number of zeros and a non-sparse matrix with a small norm that controls the estimation error bound. As no restriction is imposed on the moments of the errors, the results apply to cases when the errors have heavy- or fat-tails. In Chapter 3, I consider nuclear norm penalized quantile regression for large N and large T panel data models with interactive fixed effects. As the interactive fixed effects form a low-rank matrix, inspired by the median-zero interpretation, the estimator in this chapter extends the one studied in Chapter 2 by incorporating a conditional quantile restriction given covariates. The estimator solves a global convex minimization problem, not requiring pre-estimation of the (number of the) fixed effects. Uniform rates are obtained for both the slope coefficients and the low-rank common component of the interactive fixed effects. The rate of the latter is nearly optimal. To derive the rates, I show new results that establish uniform bounds of norms of certain random matrices of jump processes. The performance of the estimator is illustrated by Monte Carlo simulations.

In some survival analysis of medical studies, there are often long term survivors who can be considered as permanently cured. The goals in these studies are to estimate the cure probability of the whole population and the hazard rate of the noncured subpopulation. The existing methods for cure rate models have been limited to parametric and semiparametric models. More specifically, the hazard function part is estimated by parametric or semiparametric model where the effect of covariate takes a parametric form. And the cure rate part is often estimated by a parametric logistic regression model. We introduce a non-parametric model employing smoothing splines. It provides non-parametric smooth estimates for both hazard function and cure rate. By introducing a latent cure status variable, we implement the method using a smooth EM algorithm. Louis' formula for covariance estimation in an EM algorithm is generalized to yield point-wise confidence intervals for both functions. A simple model selection procedure based on the Kullback-Leibler geometry is derived for the proposed cure rate model. Numerical studies demonstrate excellent performance of the proposed method in estimation, inference and model selection. The application of the method is illustrated by the analysis of a melanoma study. / Ph. D.

Master of Science / Department of Statistics / Haiyan Wang / The purpose of this report is to numerically compare several tests that are applicable to longitudinal data when the experiment contains a large number of treatments or experimental conditions. Such data are increasingly common as technology advances. Of interest is to evaluate if there is any significant main effect of treatment or time, and their interactions. Traditional methods such as linear mixed-effects models (LME), generalized estimating equations (GEE), Wilks' lambda, Hotelling-Lawley, and Pillai's multivariate tests were developed under either parametric distributional assumptions or the assumption of large number of replications. A few recent tests, such as Zhang (2008), Bathke & Harrar (2008), and Bathke & Harrar (2008) were specially developed for the setting of large number of treatments with possibly small replications. In this report, I will present some numerical studies regarding these tests. Performance of these tests will be presented for data generated from several distributions.

This dissertation presents an exploration of the use of nonparametric statistical methods based on ranks for use in financial market research. Applications to event study methodology and the estimation of security systematic risk are analyzed using a simulation methodology with actual daily security return data. The results indicate that procedures based on ranks are more efficient than normal theory procedures currently in common use.

published_or_final_version / abstract / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / abstract / Computer Science / Master / Master of Philosophy