The Application Of Local Polynomial Kernel Regression In The Zero-inflated Poisson Model

Count data is a special kind of discrete data, which has an important significance on the study of statistical models. Therefore, it is necessary for us to study count data models deeply. From poisson regression model to zero-inflated poisson regression model, and from negative binomial regression model to zero-inflated negative binomial regression model, our discussion is more and more comprehensive, and more and more delicate.The estimation of parameters is one key of mathematical statistics, and the method of solving it can be divided into two classes. The one is parametric, the other is nonparametric. Comparatively speaking, the nonparametric method has less restrictions on the regression function. Besides, it gets better results. So the nonparametric method has a wide application. The local polynomial kernel regression is a kind of nonparametric methods, and it estimates the function at each point. Moreover, the local polynomial kernel regression involves less parameters. As long as proper kernel function K() and bandwidth h are selected, it is believable that the local polynomial kernel regression can obtain good fitting effects in the zero-inflated poisson regression model.The zero-inflated poisson regression model is a kind of finite mixture models, and it achieves a very good effect on analyzing count datas that contain excess zeros. The zero-inflated poisson regression model has two parameters. The one is inflation probability ω, the other is poisson mean μ. This article mainly discusses the situation that ω is constant. Compared to the case that ω is a variable, what we discusses is more simple. But it rarely affects the final result. We mainly adopt EM algorithm to maximizing the likelihood function, and in that case, parameters can be estimated. For some part of the process, we have to use Newton-Raphson algorithm. It is beyond our abilities to compute iteratively, so we use computer to simulate and calculate. Because of the defects of MLE, the fitting effect of simulation curve is good at most points, but not so good at boundary points for large deviation.