Variational Bayes methods for Bayesian quantile stochastic frontier models†
Jangwon Lee1 · Dongu Han2 · Jichan Park3 · Taeryon Choi4
1234Department of Statistics, Korea University
Correspondence to: † This research was supported by a Korea University Grant (K2306961).
1 Graduate student, Department of Statistics, Korea University, Seoul 02841, Korea.
2 Graduate student, Department of Statistics, Korea University, Seoul 02841, Korea.
3 Graduate student, Department of Statistics, Korea University, Seoul 02841, Korea.
4 Professor, Department of Statistics, Korea University, Seoul 02841, Korea. E-mail: trchoi@korea.ac.kr
1 Graduate student, Department of Statistics, Korea University, Seoul 02841, Korea.
2 Graduate student, Department of Statistics, Korea University, Seoul 02841, Korea.
3 Graduate student, Department of Statistics, Korea University, Seoul 02841, Korea.
4 Professor, Department of Statistics, Korea University, Seoul 02841, Korea. E-mail: trchoi@korea.ac.kr
Received January 30, 2024; Revised February 23, 2024; Accepted March 2, 2024.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- The stochastic frontier model, which is one of a broadly used model on the efficiency of enterprises, has been consistently investigated not only in economics but also in various fields such as industry and sports. In many empirical studies using probabilistic change models, statistical inference is required not only for the average response variable but also for response variables at various quantiles, along with robust inference needed due to the non-normality and outliers of the response variables. For this purpose, this paper proposes a Bayesian quantile stochastic frontier model and investigates nonparametric Bayesian models through a Dirichlet mixture process by relaxing parametric assumptions about the inefficiency term widely used in the literature. Furthermore, this paper conducts an analysis of the proposed model using variational Bayes methods, thereby providing a faster and more efficient alternative compared to the Markov Chain Monte Carlo method. Through simulation experiments, this paper compares and analyzes the performance of the proposed model and the utility of variational Bayesian methods with the Markov Chain Monte Carlo method and it conducts empirical analysis on the efficiency of game operations for each team based on collected real data from Korea basketball league.
- Keywords : Dirichlet process mixture, model selection, quantile regression, stochastic frontier model, variational Bayes
Full Text(PDF) Free
