published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

The first essay of this dissertation studies the determinants and effects of firms' participation in a voluntary pollution reduction program (VPR) initiated by government regulators. This research presents empirical evidence in support of the "enforcement theory" for VPRs, which predicts that (1) participation is rewarded by relaxed regulatory scrutiny; (2) the anticipation of this reward spurs firms to participate in the program; and (3) the program rewards regulators with reduced pollution. The results also indicate that firms' VPR participation, and pollutant reductions themselves, were prompted by a firm's likelihood of becoming a boycott target and/or being subject to environmental interest group lobbying for tighter standards.In the second essay, a nonparametric regression estimator which can accommodate two empirically relevant data environments is proposed. The first data environment assumes that at least one of the explanatory variables is discrete. In such an environment, a "cell" approach which estimates a separate regression for each discrete cell, has generally been employed. The second data environment assumes that one needs to estimate a set of regression functions that belong to different individuals. In both environments the proposed estimator attempts to reduce estimation error by incorporating extraneous data from the other individuals or "cells" when estimating the regression function for a given individual or "cell". The simulation results for the proposed estimator demonstrate a strong potential in empirical applications.In the third essay, the nonparametric approach proposed in the second essay is used to estimate the parameters of the short-term interest rate diffusion. The nonparametric estimators of the drift of the short rate proposed by Stanton (1997) and Jiang (1998) can produce spurious nonlinearities due to the persistent dependence and limited sampling period of interest rates. The simulations show that the proposed estimator significantly attenuates the spurious nonlinearities of Stanton's nonparametric estimator. An empirical study of the US term structure of interest rates is presented based on the proposed estimator and two other competing models. The results suggest that the estimation of the short rate diffusion parameters using additional data from yields of different maturities has significant economic implications on the valuation interest rate derivatives.

In this dissertation we present a novel computational method, as well as its software implementation, to compare two samples by a nonparametric likelihood-ratio test. The basis of the comparison is a mean-type hypothesis. The software is written in the R-language [4]. The two samples are assumed to be independent. Their distributions, which are assumed to be unknown, may be discrete or continuous. The samples may be uncensored, right-censored, left-censored, or doubly-censored. Two software programs are offered. The first program covers the case of a single mean-type hypothesis. The second program covers the case of multiple mean-type hypotheses. For the first program, an approximate p-value for the single hypothesis is calculated, based on the premise that -2log-likelihood-ratio is asymptotically distributed as ­­χ2(1). For the second program, an approximate p-value for the p hypotheses is calculated, based on the premise that -2log-likelihood-ratio is asymptotically distributed as ­χ2(p). In addition we present a proof relating to use of a hazard-type hypothesis as the basis of comparison. We show that -2log-likelihood-ratio is asymptotically distributed as ­­χ2(1) for this hypothesis. The R programs we have developed can be downloaded free-of-charge on the internet at the Comprehensive R Archive Network (CRAN) at http://cran.r-project.org, package name emplik2. The R-language itself is also available free-of-charge at the same site.

This thesis presents new Bayesian nonparametric models and approaches for their development, for the problems of name disambiguation and supervised learning. Bayesian nonparametric methods form an increasingly popular approach for solving problems that demand a high amount of model flexibility. However, this field is relatively new, and there are many areas that need further investigation. Previous work on Bayesian nonparametrics has neither fully explored the problems of entity disambiguation and supervised learning nor the advantages of nested hierarchical models. Entity disambiguation is a widely encountered problem where different references need to be linked to a real underlying entity. This problem is often unsupervised as there is no previously known information about the entities. Further to this, effective use of Bayesian nonparametrics offer a new approach to tackling supervised problems, which are frequently encountered. The main original contribution of this thesis is a set of new structured Dirichlet process mixture models for name disambiguation and supervised learning that can also have a wide range of applications. These models use techniques from Bayesian statistics, including hierarchical and nested Dirichlet processes, generalised linear models, Markov chain Monte Carlo methods and optimisation techniques such as BFGS. The new models have tangible advantages over existing methods in the field as shown with experiments on real-world datasets including citation databases and classification and regression datasets. I develop the unsupervised author-topic space model for author disambiguation that uses free-text to perform disambiguation unlike traditional author disambiguation approaches. The model incorporates a name variant model that is based on a nonparametric Dirichlet language model. The model handles both novel unseen name variants and can model the unknown authors of the text of the documents. Through this, the model can disambiguate authors with no prior knowledge of the number of true authors in the dataset. In addition, it can do this when the authors have identical names. I use a model for nesting Dirichlet processes named the hybrid NDP-HDP. This model allows Dirichlet processes to be clustered together and adds an additional level of structure to the hierarchical Dirichlet process. I also develop a new hierarchical extension to the hybrid NDP-HDP. I develop this model into the grouped author-topic model for the entity disambiguation task. The grouped author-topic model uses clusters to model the co-occurrence of entities in documents, which can be interpreted as research groups. Since this model does not require entities to be linked to specific words in a document, it overcomes the problems of some existing author-topic models. The model incorporates a new method for modelling name variants, so that domain-specific name variant models can be used. Lastly, I develop extensions to supervised latent Dirichlet allocation, a type of supervised topic model. The keyword-supervised LDA model predicts document responses more accurately by modelling the effect of individual words and their contexts directly. The supervised HDP model has more model flexibility by using Bayesian nonparametrics for supervised learning. These models are evaluated on a number of classification and regression problems, and the results show that they outperform existing supervised topic modelling approaches. The models can also be extended to use similar information to the previous models, incorporating additional information such as entities and document titles to improve prediction.

Nonparametric procedures use weak assumptions such as continuity of the distribution so that they are applicable to a large class F of underlying distributions. Statistics that are distribution-free over F may be constructed to be estimators of location. Such estimators are derived from rank tests called R-estimators. They are robust estimators. The concept of robust estimation is based on a neighborhood of parametric models called "gross error models". The M-estimator, which is a maximum likelihood type estimator, arose from such investigations using the normal distribution. A third big class of estimators is the class of linear combinations of order statistics called L-estimators. They are constructed as an average of quantiles. Examples are the sample mean and the sample median.In this thesis, some definitions and results involving these three basic classes of estimates are provided. For each class, an example of a robust estimator is presented. Numerical values are given to assess the robustness of each estimator in terms of breakdown point and gross error sensitivity. Further, the U-statistics which are unbiased estimators of location parameters, are used to obtain asymptotically efficient R-estimates. / Department of Mathematical Sciences

This thesis explores the practical use of kernel smoothing in three areas: binary regression, density estimation and Poisson regression sample size calculations. Both nonparametric and semiparametric binary regression estimators are examined in detail, and extended to two bandwidth cases. The asymptotic behaviour of these estimators is presented in a unified way, and the practical performance is assessed using a simulation experiment. It is shown that, when using the ideal bandwidth, the two bandwidth estimators often lead to dramatically improved estimation. These benefits are not reproduced, however, when two general bandwidth selection procedures described briefly in the literature are applied to the estimators in question. Only in certain circumstances does the two bandwidth estimator prove superior to the one bandwidth semiparametric estimator, and a simple rule-of-thumb based on robust scale estimation is suggested. The second part summarises and compares many different approaches to improving upon the standard kernel method for density estimation. These estimators all have asymptotically 'better' behaviour than the standard estimator, but a small-sample simulation experiment is used to examine which, if any, can give important practical benefits. Very simple bandwidth selection rules which rely on robust estimates of scale are then constructed for the most promising estimators. It is shown that a particular multiplicative bias-correcting estimator is in many cases superior to the standard estimator, both asymptotically and in practice using a data-dependent bandwidth. The final part shows how the sample size or power for Poisson regression can be calculated, using knowledge about the distribution of covariates. This knowledge is encapsulated in the moment generating function, and it is demonstrated that, in most circumstances, the use of the empirical moment generating function and related functions is superior to kernel smoothed estimates.

Image processing applications such as image denoising, image segmentation, object detection, object recognition and texture synthesis often require a multi-scale analysis of images. This is useful because different features in the image become prominent at different scales. Traditional imaging models, which have been used for multi-scale analysis of images, have several limitations such as high sensitivity to noise and structural degradation observed at higher scales. Parametric models make certain assumptions about the image structure which may or may not be valid in several situations. Non-parametric methods, on the other hand, are very flexible and adapt to the underlying image structure more easily. It is highly desirable to have effi cient non-parametric models for image analysis, which can be used to build robust image processing algorithms with little or no prior knowledge of the underlying image content. In this thesis, we propose a non-parametric pixel neighbourhood based framework for multi-scale image analysis and apply the model to build image denoising and saliency detection algorithms for the purpose of illustration. It has been shown that the algorithms based on this framework give competitive results without using any prior information about the image statistics.

Thesis (Ph.D.)--McMaster University, 2002. / Adviser: N. Balakrishnan. Includes bibliographical references. Also available via World Wide Web.

Thesis (Ph.D.)--McMaster University, 2002. / Adviser: N. Balakrishnan. Includes bibliographical references. Also available via World Wide Web.

Thesis (M.S.)--Universidad de Puerto Rico, Recinto Universitario de Mayagüez, 2004. / Tables. Printout. Abstract in Spanish and English. Includes bibliographical references (leaves 78-82).