基于函数型主成分分析的我国城市人口研究

Research on Urban Population in China Based on Functional Principal Component Analysis

为了探讨近年来我国主要城市人口数量的变化差异,利用4次B样条基函数,将离散的原始数据拟合成连续化的函数型数据,运用L2空间上函数型主成分分析模型,对1998~2016年我国36个主要城市的人口进行了研究.结果表明:我国超一线城市和直辖市的人口基数大,远远超过了其他城市的人口数;随着时间的变化,各城市之间人口数量差异越来越大;1998~2008年间几乎每个城市的人口数量保持平稳的增长趋势,但2008年以后部分城市人口出现较为明显的波动.分析结果表明函数型主成分方法能较为准确地分析我国主要城市人口的变化特征.

In order to explore the variation of population in the main cities in our country,in recent years the 4 B spline basis functions have been used to synthesize the discrete original data to synthesize the continuous functional data.The population of the 36 major cities from 1998 to 2016 was studied by using the spatial functional principal component analysis model.The result shows that the population base of super cities and municipalities directly under the central government is large and far exceeds the number of other cities.Secondly,with the change of time,the population difference between cities is getting larger and larger;the population of almost every city in 1998-2008 has maintained a steady growth trend,however,after 2008,the population of some cities showed more obvious fluctuations.The results show that the method of functional principal component analysis can accurately analyze the changing characteristics of the main cities in China.