Ranking And Analysis Based On Functional Data Of Environment Index PM10

This paper systematically introduces ranking methods of functional data, summing up several commonly used methods, such as mean-variance weighted method, princi-pal component analysis, discrete segments ranking weighted method, and functional seg-ments ranking weighted method. The advantages and disadvantages of each method are discussed as well. The functional segments ranking weighted method is more accurate among them which allows the presence of missing values in the original data, namely, the observation does not require the time points and the number of time points are the same. And the continuation of discrete data ensures the completeness of the information, making the results more precise. Then using the statistical software SAS to simulate abnormal values and white noise data to compare the precision of these ranking methods, principal component analysis, discrete segments ranking weighted method and function-al segments ranking weighted method are included. Finally, apply functional segments ranking weighted method on the functional data of world and China’s environment index PM10 to obtain the ranking numbers, and carry on doing nonparametric rank sum test and linear regression analysis. We used to process functional data based on the mean value, here we use the ranking numbers in the linear regression analysis. Compared with the previous linear regression results, we find the R-squared value becomes much larger and more independent variables are significant, making the model better fits.