Zero-inflated Poisson Partially Linear Single-index Model With Covariates Missing At Random

Counting data is widely used in our lives.It is a very common type of data.There are a large number of counting data in many fields such as medicine,finance,actuarial,industrial,and tourism.The Poisson regression model is the most commonly used model for processing count data.However,in practice,zero count data samples,zero-inflated data,are often encountered.For this type of data,experts proposed a zero-inflated Poisson regression model,but in the actual establishment of zero-inflated Poisson regression model,the following two situations are often encountered:covariates are sometimes not all observed,and there may be missing values.There is also a"dimensional curse" problem between multiple high-dimensional covariates.In view of the above two cases,this paper proposes a zero-inflated Poisson partial linear single-index model with covariates missing at random.In this paper,the linear single-index model of zero-inflated Poisson is firstly proposed.Secondly,the parameter estimation problem in the model is analyzed.It is divided into two parts.The first part uses the B-spline function to approximate the unknown smooth single-index function when the co-variant is not missing.Then,using the maximum likelihood estimation to obtain the estimation of each parameter in the model;the second part considers the missing of the covariate into the zero-expansion Poisson partial linear single-index model,assuming the linear part of the partial linear single-index model.The variables are randomly missing,and the parameters of the model are estimated by using the inverse probability weighting method which is more efficient and unbiased to deal with the missing data.Then,a partial linear single-index model is applied to the log-average of the Poisson part by Monte Carlo simulation,and the parameter estimation results obtained when the degree of co-variation is different and the prediction effect of the single-index function are analyzed.Finally,a preliminary outlook is given for the research of this paper.