Application And Analysis Of Natural Cubic Spline In Zero-One Inflated Poisson Regression Model

In many fields such as insurance,risk control,psychology,biomedicine and pub-lic health,there are commonly used count data,and we often use poisson regression model and negative binomial distribution regression model to study the count data.However,the frequency of zero-one is much higher than the probability of zero-one in poisson regression model,so we call this kind of data zero-one inflated data.If we use the original method to study zero-one inflated data,there will be a great deviation.In recent years,a zero-one-inflated model(ZOIP)was proposed to fit and study this kind of data.In this paper,we mainly use the nonparametric method to estimate the pa-rameters of zero-one inflated model.The nonparametric estimation method is an important direction of the development of modern statistics in the last two decades.The nonparametric model makes no assumptions about the population distribution and is not restricted by the population distribution,but knows that the popula-tion is a random variable.The nonparametric model is robust compared with the parametric model.The nonparametric estimation methods include kernel regression estimation,local polynomial estimation,polynomial spline estimation and smooth spline estimation.Therefore,in this paper,the parameters of the zero-one-inflated poisson regression model is estimated by the method of natural cubic spline non-parametric method.Estimation of covariate parameters by Maximum Likelihood Method,and restrict the penalty term of likelihood function.This is the innovation of this paper.The spline is used to estimate the parameters of zero-inflated poisson regression model.When we choose natural cubic spline to estimate parameter,we need to consider "dimension evil root" in nonparametric estimation,so the order of polynomial spline is not the higher the better,so we choose natural cubic spline function to estimate parameter.This is the focus of this paper on the expansion parameters.In the process of estimation,we introduce covariables.We also use EM algorithm,penalty maximum likelihood estimation and Newton algorithm to esti-mate the parameters of covariates.Newton-Raphson approximate solution,Reinsch algorithm,through iterative algorithm,we can get the estimated value of the pa-rameters.For the penalty parameter ?,we choose the generalized cross-validation method to select the optimal penalty parameter.Finally,with limited samples,the simulation results are used to verify the feasibility of the method.