零—膨胀泊松回归模型的非参数统计分析及其应用

Nonparametric Statistical Analysis of Zero-and-One Inflated Poisson Regression Models and Its Application

零膨胀计数数据是当今数据分析的热点问题之一,该类数据的特点是零点过多,目前对这类数据的研究已经比较全面。另外还有些计数数据不仅会出现零点过多的现象,也会同时存在零、一点都过多的情形,如果再用零膨胀计数数据的统计方法去研究,产生的误差较大。目前国内外对零和一都膨胀的数据的研究还比较少,针对这种现象,本文引入零一膨胀泊松回归模型,并用局部多项式核回归法这种非参数统计分析方法对零一膨胀泊松回归模型进行参数估计,这是本文的创新点也是难点,并在求解参数的过程中引进了EM算法和Newton-Raphson迭代对参数近似求解。通过模拟结果可以得出此方法的可行性,最后通过对糖尿病患者数据的实例分析,可以验证此方法的有效性。

Zero-inflated counting data is one of the hot issues in data analysis today. This kind of data is characterized by too many zero points. At present, the research on this kind of data is quite 2 comprehensive. In addition, some counting data will not only appear excessive zero phenomenon, there will be one-inflated, and then use zero-inflated counting data to study the statistical methods, resulting in greater error. At present, there are still few researches on this kind of data at home and abroad.In view of this phenomenon, zero-and-one inflated Poisson regression model is introduced in this paper,and the non-parametric statistical analysis method of local polynomial kernel regression is applied to zero-one inflated Poisson regression model parameter estimation, which is the innovation of this paper is also difficult. In the process of solving the parameters, EM algorithm and Newton-Raphson iteration are introduced to approximate the parameters. The feasibility of this method can be obtained through simulation results. Finally, the validity of this method can be verified by analyzing the data of diabetes patients.