Modified maximum likelihood approach in uncertain regression analysis and application to factors analysis of urban air quality

Abstract

Uncertain regression analysis is an indispensable field in statistics, and it conducts in-depth research on data sets under uncertain environments based on regression models to predict and explain the relationship between variables. However, when the data set is affected by outliers, the existing research methods will no longer be effective. In order to eliminate the influence of outliers on the accuracy of uncertain regression model fitting and prediction, this paper estimates the unknown parameters and disturbance term in the uncertain regression model based on a modified maximum likelihood idea, and provides a numerical algorithm to solve the specific estimator. Subsequently, two numerical examples are also provided to illustrate the modified maximum likelihood approach proposed in this paper and its effectiveness compared with the existing maximum likelihood method. Finally, this paper applies the proposed approach to the factor analysis of Shenzhen’s air quality, and successfully reveals the key factors affecting Shenzhen’s air quality, which provides a scientific basis for the subsequent management strategy.