Three essays on nonparametric and semiparametric regression models

This dissertation contains three essays on nonparametric and semiparametric regression models.; In the first essay, we propose an estimation procedure for value at risk (VaR) and expected shortfall (TailVaR) for conditional distributions of a time series of returns on a financial asset. Our approach combines a local polynomial estimator of conditional mean and volatility functions in a conditional heterocedastic autoregressive nonlinear (CHARM) model with Extreme Value Theory for estimating quantiles of the conditional distribution. We investigate the finite sample properties of our method and contrast them with alternatives, including the method recently proposed by McNeil and Frey (2000), in an extensive Monte Carlo study. The method we propose outperforms the estimators currently available in the literature.; In the second essay, we propose a nonparametric regression frontier model that assumes no specific parametric family of densities for the unobserved stochastic component that represents efficiency in the model. Nonparametric estimation of the regression frontier is obtained using a local linear estimator that is shown to be consistent and nhn asymptotically normal under standard assumptions. The estimator we propose envelops the data but is not inherently biased as Free Disposal Hull - FDH or Data Envelopment Analysis - DEA estimators. It is also more robust to extreme values than the aforementioned estimators. A Monte Carlo study is performed to provide preliminary evidence on the estimator's finite sample properties and to compare its performance to a bias corrected FDH estimator.; In the third essay, we establish the n asymptotic equivalence of V and U statistics when the statistic kernel depends on n. Combined with a lemma of Lee (1988) this result provides conditions under which U statistics projections (Hoeffding, 1961) and V statistics are n asymptotically equivalent. The use of this equivalence in nonparametric regression models is illustrated with two examples. The estimation of conditional variances and construction of nonparametric R-square.