Regression Under Nonlinear Expectation And Its Applications

Classic al probabilistic statistical model are mainly good at dealing with the problem with distributed certainty,where the probability distribution function or density function of a random variable is known or assumed,and are widely used in various fields.With the continuous deepening of research,it is found that the certainty distribution assumptions are usually no longer satisfied,and thus the risks is difficult to predict and control.Regarding how to deal with statistical problems with distribution uncertainty,Peng jumped out of the classical probability system and constructed nonlinear expectation theory system.He pointed out that nonlinear expectation theory can perform robust quantitative analysis and calculation on probabilistic statistical problems when the probability model itself cannot be determined,that is,when there is distribution uncertainty.Linear regression model is one of the most used models in classical probability statistics.However,when the model has distribution uncertainty,classical linear regression models are no longer valid.This paper mainly studies regression models under the sublinear expectation.Based on existing research,this paper present a method for solving the explicit solution in the case of a single variable is proposed,and for the general multidimensional case of multiple variables,the Nelder-Mead method is proposed for solving.it improves the accuracy of parameter estimation,avoids common problems in numerical methods,and improves the usability of the model.Finally,this paper simulates the generation of data with varying degrees of distribution uncertainty and empirical analysis of factors affecting the NPL rate,pointing out that under distribution uncertainty,the regression model under sublinear expectations can still provide relatively accurate statistical analysis results,it is shown that in the analysis of real data with distribution uncertainty,the regression model under sublinear expectations can still provide relatively effctive statistical results,which has certain advantages compared to the classical linear regression analysis.And the effectiveness of the regression model under the sublinear expectation framework under the real data is verified.