基于两部模型的组合惩罚似然估计方法研究及其应用

Research and Application of Combined Penalty Likelihood Estimation Method Based on Two-Part Model

摘要: 在统计学中，多借助零膨胀模型研究零膨胀数据潜在的模型结构及变量选择问题。然而，在多数情况下，响应变量的非零部分为定量数据，简单的零膨胀模型无法刻画这类数据的模型结构，对应的参数估计方法也不再适用。鉴于此，学者提出处理零膨胀半连续数据的两部模型。本文将组合惩罚似然估计方法引入两部模型，研究其变量选择问题。提出一种新的处理高维统计分析问题的惩罚似然估计方法：NCPM (New Combined Punishment Method)，并将该方法应用于太原市降水量数据，分析其影响因素。模拟及实例分析结果均表明本文的方法行之有效，较传统的惩罚似然估计方法具有更高的预测精度。

Abstract: In statistics, the potential model structure and variable selection problems of zero expansion data are often studied by means of zero expansion model. However, in most cases, the non-zero part of the response variable is quantitative data. A simple zero expansion model cannot describe the model structure of such data, and the corresponding parameter estimation method is no longer applicable. In view of this, scholars proposed a two-part model to deal with zero expansion semi-continuous data. In this paper, the combined penalty likelihood estimation method is introduced into the two-part model to study the problem of variable selection. A new penalty likelihood estimation method, NCPM (New Combined Punishment Method), is proposed to deal with high-dimensional statistical analysis problems. The method is applied to Taiyuan precipitation data and its influencing factors are analyzed. The results of simulation and case analysis show that the proposed method is effective and has higher prediction accuracy than the traditional penalty likelihood estimation method.