Nonparametric estimation of econometric models with categorical variables
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In this dissertation I investigate several topics in the field of nonparametric econometrics. In chapter II, we consider the problem of estimating a nonparametric regression model with only categorical regressors. We investigate the theoretical properties of least squares cross-validated smoothing parameter selection, establish the rate of convergence (to zero) of the smoothing parameters for relevant regressors, and show that there is a high probability that the smoothing parameters for irrelevant regressors converge to their upper bound values thereby smoothing out the irrelevant regressors. In chapter III, we consider the problem of estimating a joint distribution defined over a set of discrete variables. We use a smoothing kernel estimator to estimate the joint distribution, allowing for the case in which some of the discrete variables are uniformly distributed, and explicitly address the vector-valued smoothing parameter case due to its practical relevance. We show that the cross-validated smoothing parameters differ in their asymptotic behavior depending on whether a variable is uniformly distributed or not. In chapter IV, we consider a k-n-n estimation of regression function with k selected by a cross validation method. We consider both the local constant and local linear cases. In both cases, the convergence rate of of the cross validated k is established. In chapter V, we consider nonparametric estimation of regression functions with mixed categorical and continuous data. The smoothing parameters in the model are selected by a cross-validation method. The uniform convergence rate of the kernel regression function estimator function with weakly dependent data is derived.
Ouyang, Desheng (2005). Nonparametric estimation of econometric models with categorical variables. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from