arXiv subjects

Xibin Zhang

Publications and source records attributed to Xibin Zhang.

3 recordsLinked to original sources

arXiv2026

Panel Stochastic Frontier Models with Latent Group Structures

Stochastic frontier models have attracted considerable attention due to the incorporation of an inefficiency term in addition to the conventional error term. In this paper, we propose a general estimation framework for panel stochastic frontier models that accommodates potential heterogeneity through latent group structures. The framework is tailored to the distinctive features of stochastic frontier models and is paired with a practical hybrid estimation procedure that combines individual-level and joint panel estimation. We illustrate the estimation framework using a panel stochastic frontier model that treats the inefficiency term as a random effect, and show that it can be readily extended to a range of fixed effects specifications common in the literature. Simulation studies indicate strong finite-sample performance, and we further demonstrate the practicality of the approach in an empirical application to the cost efficiency of the U.S. commercial banking sector.

econ.EM↗

arXiv2022

A flexible method for estimating luminosity functions via Kernel Density Estimation -- II. Generalization and Python implementation

We propose a generalization of our previous KDE (kernel density estimation) method for estimating luminosity functions (LFs). This new upgrade further extend the application scope of our KDE method, making it a very flexible approach which is suitable to deal with most of bivariate LF calculation problems. From the mathematical point of view, usually the LF calculation can be abstracted as a density estimation problem in the bounded domain of $\{Z_1 f_{\mathrm{lim}}(z) \}$. We use the transformation-reflection KDE method ($\hatϕ$) to solve the problem, and introduce an approximate method ($\hatϕ_{\mathrm{1}}$) based on one-dimensional KDE to deal with the small sample size case. In practical applications, the different versions of LF estimators can be flexibly chosen according to the Kolmogorov-Smirnov test criterion. Based on 200 simulated samples, we find that for both cases of dividing or not dividing redshift bins, especially for the latter, our method performs significantly better than the traditional binning method $\hatϕ_{\mathrm{bin}}$. Moreover, with the increase of sample size $n$, our LF estimator converges to the true LF remarkably faster than $\hatϕ_{\mathrm{bin}}$. To implement our method, we have developed a public, open-source Python Toolkit, called \texttt{kdeLF}. With the support of \texttt{kdeLF}, our KDE method is expected to be a competitive alternative to existing nonparametric estimators, due to its high accuracy and excellent stability. \texttt{kdeLF} is available at \url{http://github.com/yuanzunli/kdeLF} with extensive documentation available at \url{http://kdelf.readthedocs.org/en/latest~}.

astro-ph.IM↗

arXiv2020

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 et al., 2014). While Zhang et al. (2014) 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.

stat.ME↗