Nonparametric panel data regression with parametric cross-sectional dependence

In this paper, we consider efficiency improvement in a nonparametric panel data model with cross-sectional dependence. A Generalized Least Squares (GLS)-type estimator is proposed by taking into account this dependence structure. Parameterizing the cross-sectional dependence, a local linear estimator is shown to be dominated by this type of GLS estimator. Also, possible gains in terms of rate of convergence are studied. Asymptotically optimal bandwidth choice is justified. To assess the finite sample performance of the proposed estimators, a Monte Carlo study is carried out. Further, some empirical applications are conducted with the aim of analyzing the implications of the European Monetary Union for its member countries.

Bayesian bandwidth estimation for local linear fitting in nonparametric regression models

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 location-mixture 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 kernel-form 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: 218–34.). 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: 218–34) use the local constant (also known as the Nadaraya-Watson) 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 data-driven methods for simultaneously choosing bandwidths in the local linear estimator of the regression function and kernel-form 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 rule-of-thumb and cross-validation 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 state-price density estimation.

Identification the number of Mycobacterium tuberculosis based on sputum image using local linear estimator

Infectious disease caused by infection of Mycobacterium tuberculosis is called tuberculosis (TB). A common method in detecting TB is by identifying number of mycobacterium TB in sputum manually. Unfortunately, manually calculation by pathologists take a relatively long time. Previous researches on TB bacteria were still limited to detect the absence or presence of mycobacterium TB in images of sputum. This research aims are identifying number of mycobacterium TB and determining accuracy of classification TB severity by approaching nonparametric Poisson regression model and applying an estimator namely local linear. Steps include processing of image, reducing of dimension by applying partial least square and discrete wavelet transformation, and then identifying the number of mycobacterium TB by using the proposed model approach. In this research, we get deviance values of 28.410 for nonparametric and 93.029 for parametric approaches and the average of classification accuracy values for 4 iterations of 92.75% for nonparametric and 85.5% for parametric approaches. Thus, for identifying many of mycobacterium TB met in images of sputum and classifying of TB severity, the proposed identifying method gives higher accuracy and shorter time in identifying number of mycobacterium TB than parametric linear regression method.