Finite sample performance of nonparametric regression estimators : the case of additive and parametric covariance models

• Main Author: Yang, Ke
• Other Authors: Martins-Filho, Carlos
• Language: en_US
• Published: 2012
• Subjects: Nonparametric statistics; Estimation theory
• Online Access: http://hdl.handle.net/1957/28595

This dissertation is composed of three essays regarding the finite sample properties of estimators for nonparametric models. In the first essay we investigate the finite sample performances of four estimators for additive nonparametric regression models - the backfitting B-estimator, the marginal integration M-estimator and two versions of a two stage 2S-estimator, the first proposed by Kim, Linton and Hengartner (1999) and the second which we propose in this essay. We derive the conditional bias and variance of the 2S estimators and suggest a procedure to obtain optimal bandwidths that minimize an asymptotic approximation of the mean average squared errors (AMASE). We are particularly concerned with the performance of these estimators when bandwidth selection is done based on data driven methods. We compare the estimators' performances based on various bandwidth selection procedures that are currently available in the literature as well as with the procedures proposed herein via a Monte Carlo study. The second essay is concerned with some recently proposed kernel estimators for panel data models. These estimators include the local linear estimator, the quasi-likelihood estimator, the pre-whitening estimators, and the marginal kernel estimator. We focus on the finite sample properties of the above mentioned estimators on random effects panel data models with different within-subject correlation structures. For each estimator, we use the asymptotic mean average squared errors (AMASE) as the criterion function to select the bandwidth. The relative performance of the test estimators are compared based on their average squared errors, average biases and variances. The third essay is concerned with the finite sample properties of estimators for nonparametric regression models with autoregressive errors. The estimators studied are: the local linear, the quasi-likelihood, and two pre-whitening estimators. Bandwidths are selected based on the minimization of the asymptotic mean average squared errors (AMASE) for each estimator. Two regression functions and multiple variants of autoregressive processes are employed in the simulation. Comparison of the relative performances is based mainly on the estimators' average squared errors (ASE). Our ultimate objective is to provide an extensive finite sample comparison among competing estimators with a practically selected bandwidth. === Graduation date: 2006