Projects per year
Abstract
This paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by a locationmixture density of Gaussian densities with means the individual errors and variance a constant parameter. This mixture density has the form of a kernel density estimator of errors and is referred to as the kernelform error density (c.f. Zhang, X., M. L. King, and H. L. Shang. 2014. "A Sampling Algorithm for Bandwidth Estimation in a Nonparametric Regression Model with a Flexible Error Density."Computational Statistics & Data Analysis 78: 21834.). While (Zhang, X., M. L. King, and H. L. Shang. 2014. "A Sampling Algorithm for Bandwidth Estimation in a Nonparametric Regression Model with a Flexible Error Density."Computational Statistics & Data Analysis 78: 21834) use the local constant (also known as the NadarayaWatson) estimator to estimate the regression function, we extend this to the local linear estimator, which produces more accurate estimation. The proposed investigation is motivated by the lack of datadriven methods for simultaneously choosing bandwidths in the local linear estimator of the regression function and kernelform error density. Treating bandwidths as parameters, we derive an approximate (pseudo) likelihood and a posterior. A simulation study shows that the proposed bandwidth estimation outperforms the ruleofthumb and crossvalidation methods under the criterion of integrated squared errors. The proposed bandwidth estimation method is validated through a nonparametric regression model involving firm ownership concentration, and a model involving stateprice density estimation.
Original language  English 

Pages (fromto)  5571 
Number of pages  17 
Journal  Studies in Nonlinear Dynamics and Econometrics 
Volume  26 
Issue number  1 
DOIs  
Publication status  Published  Feb 2022 
Keywords
 kernelform error density
 Markov chain Monte Carlo
 ownership concentration
 stateprice density
Projects
 2 Finished

Trending Time Series Models with Non and SemiParametric Methods
Gao, J., Zhang, X. & Tjostheim, D.
Australian Research Council (ARC), Monash University
3/01/13 → 21/03/16
Project: Research

Nonparametric Estimation of Regression Models with Unknown Error Distributions
Australian Research Council (ARC), Monash University
4/01/10 → 31/12/13
Project: Research