In this dissertation I investigate several topics in the field of nonparametric econometrics.In chapter II, we consider the problem of estimating a nonparametric regressionmodel with only categorical regressors. We investigate the theoretical propertiesof least squares cross-validated smoothing parameter selection, establish the rate ofconvergence (to zero) of the smoothing parameters for relevant regressors, and showthat there is a high probability that the smoothing parameters for irrelevant regressorsconverge to their upper bound values thereby smoothing out the irrelevant regressors.In chapter III, we consider the problem of estimating a joint distribution definedover a set of discrete variables. We use a smoothing kernel estimator to estimate thejoint distribution, allowing for the case in which some of the discrete variables areuniformly distributed, and explicitly address the vector-valued smoothing parametercase due to its practical relevance. We show that the cross-validated smoothingparameters differ in their asymptotic behavior depending on whether a variable isuniformly distributed or not.In chapter IV, we consider a k-n-n estimation of regression function with k selectedby 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 withmixed categorical and continuous data. The smoothing parameters in the model areselected by a cross-validation method. The uniform convergence rate of the kernelregression function estimator function with weakly dependent data is derived.
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