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Investment, consumption and export are the troika which promotes China's economic development. Investment is the most important factor and plays a vital role to drive economic growth. However, due to the differences in the geographical location, education level and infrastructure construction of various regions in China, the structure of economic development and the imbalance of growth still exist. This paper takes the fixed asset investment of 31 provinces, municipalities and autonomous regions in my country from 1999 to 2017 as the research objects in our country and uses functional data analysis methods to functionalize discrete data, uses Fourier basis functions to fit the smooth curve, and then uses FPCA analysis of the characteristics of the principal component function shows that the contribution rates of the first two principal components to the regional economy are 96.4% and 2.8% respectively, and the cumulative contribution rate reaches 99.2%, which can represent most of the sample information to a certain extent. Therefore, this paper uses the first two main components to analyse the overall change for law of China's regional economy, and roughly divides my country's 31 provinces and municipalities into 4 categories and adjust my country's economic development structure and promote coordinated regional development.

Analysis of the regional differences between fixed assets investment and China's economic growth from the perspective of functional data