单指标众数模型的统计诊断及在波士顿房价分析中的应用

The Statistical Diagnosis Based on Single Index Modal Regression Models and Application to Boston Data Analysis

在金融、经济、社会科学、气候科学、环境科学、工程技术和生物医学等领域,数据分布常常呈现出尖峰厚尾的特征,且密度分布是不对称的有偏分布。此时,单指标众数模型是刻画这些特征的一个重要方法。为此,非常有必要研究该模型下的统计诊断。本文将考虑单指标众数模型基于数据删除模型和众数漂移模型的统计诊断与局部影响分析。模拟研究和波士顿房价数据的结果表明所提出的方法是有效和可行的。

In the financial, economic, social science, climate science, environmental science, engineering and biomedical sciences, data distribution often shows the characteristics of higher peak and fat tail, and the density distribution is asymmetric distribution of biased. At this case, the single index modal model is an important way to describe these features. Thus, it is very necessary to research statistical diagnosis of the model. In this paper, we are going to investigate the statistical diagnosis of the single index modal model based on data deleted model and mode drift model, and local influence analysis. The simulation studies and a real example about a famous Boston housing data are conducted to illustrate the finite sample performance of the proposed method. The results show that this method is useful and effective.