Estimation Methods And Applications Of Non-parametric Spatial Random Frontier Model

The stochastic frontier model is one of the methods for measuring technical efficiency,providing scientific basis for decision-making units to adjust input decisions and achieve maximum output.However,in the classical stochastic frontier model,all decision-making units are not related to each other,and the wrong assumptions in the form of production function will lead to large errors in the measurement results of technical efficiency.Therefore,it is of practical significance to study the non-parametric spatial stochastic frontier model.This article studies the estimation methods and applications of non-parametric spatial stochastic frontier models.The first chapter mainly introduces the research background,significance,and current research status of stochastic frontier models.It briefly describes the research content and innovation points of this article,and provides preliminary knowledge related to this study.The second chapter mainly studies the generalized moment estimation of non-parametric spatial lagged stochastic frontier models.Firstly,using the generalized moment estimation method,the estimation process of a non-parametric spatial lagged stochastic frontier model is derived.Secondly,the Chebyshev inequality is used to prove that the functions in the decomposition formula of local polynomial estimation results are bounded in probability,the consistency of the coefficient of the spatial lag term and the consistency of the non-parametric model.The Chebyshev inequality and Cauchy Schwartz inequality are used to prove the consistency of the coefficient of the spatial lag term of random errors,the variance of the random Error term and the variance of the invalid rate term.Finally,numerical simulations indicate that the estimation performance of the target model is stable and the estimation accuracy improves with increasing sample size.The third chapter mainly studies Bayesian estimation of non-parametric spatial stochastic frontier models.Using the multivariate B-spline method and Bayesian estimation method,the estimation process of non-parametric spatial lag error autocorrelation random frontier model and non-parametric dynamic spatial random frontier model is derived.Numerical simulations have shown that multivariate B-splines have good fitting ability,and the estimation accuracy of the non-parametric spatial random frontier model increases with the increase of sample size.The estimation accuracy of the technical inefficiency term of the non-parametric spatial lag error autocorrelation random frontier model is higher under the single element MH sampling method,while the estimation accuracy of the technical inefficiency term of the non-parametric dynamic spatial random frontier model is lower under Gibbs sampling.The fourth chapter mainly studies the application of non-parametric spatial stochastic frontier models.Using the non-parametric spatial lag random frontier model to calculate the average technological efficiency of the fruit industry in various regions of China from 2011 to2020,and using the non-parametric spatial lag error autocorrelation random frontier model to calculate the technological efficiency of the fruit industry in various regions of China in 2020.Analyze the advantages and disadvantages of two model estimation methods in practical applications.Compared with the Bayesian estimation of non-parametric spatial lag error autocorrelation random frontier models,the GMM estimation of non-parametric spatial lag random frontier models has higher credibility in practical applications.