Browsing by Subject "Nonparametric"
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Item Limited Dependent Variable Correlated Random Coefficient Panel Data Models(2012-10-19) Liang, ZhongwenIn 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.Item Nonparametric Inference for High Dimensional Data(2013-04-23) Mukhopadhyay, SubhadeepLearning 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.Item Regression : when a nonparametric approach is most fitting(2012-05) Claussen, Pauline Elma Clara; Brockett, PatrickThis paper aims to demonstrate the benefits of adopting a nonparametric regression approach when the standard regression model is not appropriate; it also provides an overview of circumstances where a nonparametric approach might not only be beneficial, but necessary. It begins with a historical background on regression, leading into a broad discussion of the standard linear regression model assumptions. Following are particular methods to handle assumption violations which include nonlinear transformations, nonlinear parametric model fitting, and, finally, nonparametric methods. The software package, R, is used to illustrate examples of nonparametric regression techniques for continuous variables and a brief overview is given of procedures to handle nonparametric regression models that include categorical variables.Item Teacher Certification Exams: Predicting Failure on the TExES History (8-12) Content Exam (A Nonparametric Approach using Classification Trees)(2011-05) Gard, Dwight R.; Simpson, Douglas J.; Murray, John P.; Wang, Eugene W.; Tipton, Pamela E.Previous research efforts concerning teacher certification in Texas focused primarily on the Pedagogy and Professional Responsibilities exam; an exam that all teacher candidates must pass regardless of their specific content area. Few studies have attempted to explore which variables are useful for predicting the outcome of the TExES content-area certification exams, which represents a major gap in the literature. Because of its high failure rate, this study focused on identifying factors that were influential in predicting failure on the TExES History (8-12) certification exam. A convenience sample was used and only those who had taken the TExES History (8-12) exam from 2002 – 2008 were selected (n = 181). The study is an exploratory data design using classification trees—a nonparametric statistical technique often associated with data mining. The study was different from previous studies in two important aspects: a) the study included a much wider range of variables, and b) nonparametric, classification tree methodology was used to build predictive models. Using the proportional chance criterion and Press’ Q to assess significance, the models were statistically significant (p < .05), indicating that the models were capable of predicting outcomes well beyond what would be expected based on chance. Because classification trees produce a set of decision rules that can be graphically depicted, a model based on a decision tree paradigm is more intuitive, and more easily interpreted and implemented compared to regression methods. Although classification trees are not widely used in social science research, the success of the technique in the current study suggests that classification trees can be an effective, nonparametric alternative to the more traditional multiple regression and logistic regression methods and provides researchers a glimpse of the capabilities of classification trees.