Parameter Estimation Of Set-valued And Fuzzy Set-valued Spatial Error Models

There are many random phenomena in the real world.Most of the classical linear regression and time series models are statistical inference of single valued random variables.In life,people tend to pay more attention to the data in a certain range.At the same time,there are a large number of fuzzy phenomena in life.Compared with single valued random variables,Set-valued random variables and fuzzy set-valued random variables contain more available information.Many scholars have studied the classical linear regression and time series models of set-valued and fuzzy set-valued random variables,but there is little research on spatial regression models,especially spatial error models.This thesis attempts to generalize the classical spatial error model on set-valued and fuzzy set-valued random variables.Firstly,we systematically summarize the basic knowledge of set-valued and fuzzy set-valued random variables,and have a basic grasp of spatial error model.In addition,we have a deeper understanding of the algorithm and corresponding distance between set-valued and fuzzy set-valued random variables.Secondly,on the premise of mastering the basic knowledge,the definition of interval valued spatial error model is given.Based on the set-valued dp-distance and combined with the theoretical idea of least square method,the specific form of parameter estimation is given,and the unbiasedness,consistency and a series of digital characteristics of the obtained estimation are obtained;The definition of fuzzy set-valued spatial error model is given.Based on the fuzzy distance and the theoretical idea of least square method,the specific form of parameter estimation is given,and the uncorrelation of the obtained parameter estimation is proved.Then,the process of parameter estimation of interval value spatial error model is displayed through numerical simulation,and the mean square error of parameter estimation obtained by the model is calculated based on the dp-distance of interval value.Finally,it shows that the parameter estimation effect is good and has certain excellence.Finally,the index data of 31 provinces,cities and autonomous regions in China are selected to study the effects of latitude,maximum and minimum temperature and temperature difference in different regions,so as to further illustrate the application of interval value spatial error model in practice.