基于MCMC方法的单指标众数模型Bayes估计

Bayesian Estimation of Single Index Modal Model Based on MCMC Method

将单指标模型和众数回归模型相结合,构造一种新的模型——单指标众数模型,详细给出了单指标众数模型的定义,为了对模型的参数进行Bayes估计,设定了该模型的参数先验分布,然后利用MCMC方法模拟参数的后验分布,并用参数的后验均值作为参数的估计值,将参数的估计值和真值进行比较后,发现估计的效果非常好。最后,随机模拟和实际例子的分析表明所提出的模型和方法是行之有效的。

In this paper,a new model,single index modal model,is constructed by combining the single index model with modal regression.The mathematical definition of the single index modal model is given in detail.In order to estimate the coefficients of the model,the prior distribution of the model parameters is set and then the MCMC method is used to simulate the posterior distribution of the parameters.The posterior mean of the parameters is calculated as the estimated value of the parameters,the estimated value of the parameters is compared with the true value,and the estimation effect is found to be very good.Finally,a simulation study and a real example indicates that the proposed model and method are feasible.