Learning from data, especially ‘Big Data’, is becoming increasingly popular under names such as Data Mining, Data Science, Machine Learning, Statistical Learning and High Dimensional Data Analysis. In this dissertation we propose a new related field, which we call ‘United Nonparametric Data Science’ - applied statistics with “just in time” theory. It integrates the practice of traditional and novel statistical methods for nonparametric exploratory data modeling, and it is applicable to teaching introductory statistics courses that are closer to modern frontiers of scientific research. Our framework includes small data analysis (combining traditional and modern nonparametric statistical inference), big and high dimensional data analysis (by statistical modeling methods that extend our unified framework for small data analysis). The first part of the dissertation (Chapters 2 and 3) has been oriented by the goal of developing a new theoretical foundation to unify many cultures of statistical science and statistical learning methods using mid-distribution function, custom made orthonormal score function, comparison density, copula density, LP moments and comoments. It is also examined how this elegant theory yields solution to many important applied problems. In the second part (Chapter 4) we extend the traditional empirical likelihood (EL), a versatile tool for nonparametric inference, in the high dimensional context. We introduce a modified version of the EL method that is computationally simpler and applicable to a large class of “large p small n” problems, allowing p to grow faster than n. This is an important step in generalizing the EL in high dimensions beyond the p ≤ n threshold where the standard EL and its existing variants fail. We also present detailed theoretical study of the proposed method.

This dissertation, which consists of three essays, studies three applications. Each of them emphasizes the microfoundations of economic models. The first essay proposes a nonparametric estimation of structural labor supply and exact welfare change under nonconvex piecewise-linear budget sets. Different from previous literature, my method focuses on a nonparametric specification of an indirect utility function. I find that working with the indirect utility function is very useful in simultaneously addressing the labor supply problems with individual heterogeneity, nonconvex budget sets, labor nonparticipation, and measurement errors in working hours that previous literature was unable to. Further, the estimated indirect utility function proves to be convenient and efficient in calculating exact welfare change and deadweight loss under general piecewise-linear budget sets. In the second essay, I solve the equity premium, risk-free rate, and capital structure puzzles by laying a more solid microfoundation for consumption-based asset pricing models. I argue that the above two asset pricing puzzles arise from the aggregation of hump-shaped life-cycle consumption into per capita consumption, which accounts for the unanimous rejections of Euler equations in the literature. As for the third puzzle, I show that a firm's capital structure can be determined by heterogenous investors maximizing life-time utility even though the capital structure is irrelevant on the firm side. The endogenously determined leverage generates an even larger equity premium than a fixed one. The third essay studies the solution concepts of coalition equilibrium. Traditional solution concepts such as Strong Nash Equilibrium, Coalition-proof Nash Equilibrium, Largest Consistent Set, and Coalition Equilibrium violate the fundamental principles of individual rationality. I define a new solution concept, Weak Coalition Equilibrium, which requires each coalitional deviation to be within-coalition self-enforceable and cross-coalition self-enforceable. The cross-coalition self-enforceability endows coalitions with farsightedness. Weak Coalition Equilibrium is a generalization of Coalition-proof Nash Equilibrium and a re nement of the concept Nash Equilibrium. It exists under a weak condition. Most importantly, it is in line with the principle of individual rationality.

In this dissertation, I consider linear, binary response correlated random coefficient (CRC) panel data models and a truncated CRC panel data model which are frequently used in economic analysis. I focus on the nonparametric identification and estimation of panel data models under unobserved heterogeneity which is captured by random coefficients and when these random coefficients are correlated with regressors. For the analysis of linear CRC models, I give the identification conditions for the average slopes of a linear CRC model with a general nonparametric correlation between regressors and random coefficients. I construct a sqrt(n) consistent estimator for the average slopes via varying coefficient regression. The identification of binary response panel data models with unobserved heterogeneity is difficult. I base identification conditions and estimation on the framework of the model with a special regressor, which is a major approach proposed by Lewbel (1998, 2000) to solve the heterogeneity and endogeneity problem in the binary response models. With the help of the additional information on the special regressor, I can transfer a binary response CRC model to a linear moment relation. I also construct a semiparametric estimator for the average slopes and derive the sqrt(n)-normality result. For the truncated CRC panel data model, I obtain the identification and estimation results based on the special regressor method which is used in Khan and Lewbel (2007). I construct a sqrt(n) consistent estimator for the population mean of the random coefficient. I also derive the asymptotic distribution of my estimator. Simulations are given to show the finite sample advantage of my estimators. Further, I use a linear CRC panel data model to reexamine the return from job training. The results show that my estimation method really makes a difference, and the estimated return of training by my method is 7 times as much as the one estimated without considering the correlation between the covariates and random coefficients. It shows that on average the rate of return of job training is 3.16% per 60 hours training.

As concern grows about energy and environment issues, energy and environmental modeling and related policy analysis are critical issues for today's society. Polluting firms such as coal power plants play an important role in providing electricity to drive the U.S. economy as well as producing pollution that damages the environment and human health. This dissertation is intended to model and estimate polluting firms' production using nonparametric methods. First, frontier production function of polluting firms is characterized by weak disposability between outputs and pollutants to reflecting the opportunity cost to reduce pollutants. The StoNED method is extended to estimate a weak disposability frontier production function accounting for random noise in the data. The method is applied to the U.S. coal power plants under the Acid Rain Program to find the average technical inefficiency and shadow price of SO2 and NOx. Second, polluting firms' production processes are modeled characterizing both the output production process and the pollution abatement process. Using the law of conservation of mass applied to the pollution abatement process, this dissertation develops a new frontier pollutant function which then is used to find corresponding marginal abatement cost of pollutants. The StoNEZD method is applied to estimate a frontier pollutant function considering the vintage of capital owned by the polluting firms. The method is applied to estimate the average NOx marginal abatement cost for the U.S. coal power plants under the current Clean Air Interstate Rule NOx program. Last, the effect of a technical change on marginal abatement costs are investigated using an index decomposition technique. The StoNEZD method is extended to estimate sequential frontier pollutant functions reflecting the innovation in pollution reduction. The method is then applied to estimate a technical change effect on a marginal abatement cost of the U.S. coal power plants under the current Clean Air Interstate Rule NOx program.

The underlying aim of this research is to investigate the mathematical descriptions of homogeneous textures in digital images for the purpose of segmentation and recognition. The research covers the problem of testing these mathematical descriptions by using them to generate synthetic realisations of the homogeneous texture for subjective and analytical comparisons with the source texture from which they were derived. The application of this research is in analysing satellite or airborne images of the Earth's surface. In particular, Synthetic Aperture Radar (SAR) images often exhibit regions of homogeneous texture, which if segmented, could facilitate terrain classification. In this thesis we present noncausal, nonparametric, multiscale, Markov random field (MRF) models for recognising and synthesising texture. The models have the ability to capture the characteristics of, and to synthesise, a wide variety of textures, varying from the highly structured to the stochastic. For texture synthesis, we introduce our own novel multiscale approach incorporating a new concept of local annealing. This allows us to use large neighbourhood systems to model complex natural textures with high order statistical characteristics. The new multiscale texture synthesis algorithm also produces synthetic textures with few, if any, phase discontinuities. The power of our modelling technique is evident in that only a small source image is required to synthesise representative examples of the source texture, even when the texture contains long-range characteristics. We also show how the high-dimensional model of the texture may be modelled with lower dimensional statistics without compromising the integrity of the representation. We then show how these models -- which are able to capture most of the unique characteristics of a texture -- can be for the ``open-ended'' problem of recognising textures embedded in a scene containing previously unseen textures. Whilst this technique was developed for the practical application of recognising different terrain types from Synthetic Aperture Radar (SAR) images, it has applications in other image processing tasks requiring texture recognition.

Thesis (doctoral)--Göteborgs Universitet, 1993. / Errata sheet laid in. Includes bibliographical references.

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 26, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Dr. (Tony) Jianguo Sun. Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 73-77). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 73-77). Also available on the Internet.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 213-219).