We show that when estimating a nonparametric regression model, the knearest-neighbor nonparametric estimation method has the ability to remove irrelevant variables provided one uses a product weight function with a vector of smoothing parameters, and the least squares cross validation method is used to select the smoothing parameters. Simulation results are consistent with our theoretical analy...

We develop a √ n-consistent and asymptotically normal estimator of the parameters (regression coefficients and threshold points) of a semiparametric ordered response model under the assumption of independence of errors and regressors. The independence assumption implies shift restrictions allowing identification of threshold points up to location and scale. The estimator is useful in various ap...

The convolution theorem (Hájek [8]) characterizes the weak limit of any regular estimator as a convolution of two independent components. One is an optimal achievable part and another is a noise. Therefore, the optimal estimator is one without the noise part in its weak limit, which is a deeper characterization than the Cramer-Rao bound. However, this result is derived under the assumption that...

OF DISSERTATION STATISTICAL METHODS FOR ENVIRONMENTAL EXPOSURE DATA SUBJECT TO DETECTION LIMITS In this dissertation, we develop unified and efficient nonparametric statistical methods for estimating and comparing environmental exposure distributions in presence of detection limits. In the first part, we propose a kernel-smoothed nonparametric estimator for the exposure distribution without imp...

This paper develops an asymptotic theory for a general class of nonlinear nonstationary regressions, extending earlier work by Phillips and Hansen (1990) on linear cointegrating regressions.The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1) regressors. We establish consistency and derive the limit distribution of the nonlinear least squares...

The Granger}Engle procedure consists of two steps. In the "rst step, a long-run cointegrating relationship is estimated, and in the second stage, this estimated long-run relationship is used to estimate a distributed lag model. This paper establishes the limit distribution of the second-stage estimator if the model estimated in the second stage is other than linear. One may expect that the esti...

A probability is the expectation of an indicator function. However, the standard pathwise sensitivity estimation approach, which interchanges the differentiation and expectation, cannot be directly applied because the indicator function is discontinuous. In this paper, we design a pathwise sensitivity estimator for probability functions based on a result of Hong [Hong, L. J. 2009. Estimating qu...

We define a nonparametric prewhitening method for estimating conditional quantiles based on local linear quantile regression. We characterize the bias, variance and asymptotic normality of the proposed estimator. Under weak conditions our estimator can achieve bias reduction and have the same variance as the local linear quantile estimators. A small set of Monte Carlo simulations is carried out...

A martingale estimator for the expected discounted warranty cost process of a minimally repaired coherent system under its component level observation is proposed. Its asymptotic properties are also presented using the Martingale Central Limit Theorem.