Research On Approximation Properties Based On Beta Basic Function And Its Application In Regression Analysis Model

With the improvement of the level of mathematical research,more and more mathematical functions are widely used in the field of probability operator approximation.Bernstein operator was first proposed,and the approximation property of Bernstein operator has attracted more scholars’ attention since it was proposed.Then there have been many kinds of operator approximation studies,and then some scholars have applied the basis function of the operator to the field of data mining,a new data mining model,a new fitting prediction model based on Bernstein basis function,is creatively proposed,which is widely used in many fields.The first focus of this article is to further generalize the Bernstein operator and construct a new type of beta operator with parameters based on it.Finally,the related approximation problems of beta operators are discussed.The second focus is to use carbon emission time series data to construct a beta basis function model with parameters based on the Bernstein basis function model,in order to promote and improve the Bernstein basis function model.When the shape parameters tend to infinity,the beta basis function model and the Bernstein basis function model have the same fitting effect.This article is divided into four parts for elaboration:Chapter 1: In the introduction,this paper describes the background of carbon emissions from various perspectives,including the impact characteristics of carbon emissions at every corner,the important position of carbon emissions price under the background about carbon emissions,and the relevant background of probability operators and their basis functions for studying the model of new carbon emissions price.The last part is to explain the overall framework and innovation of these contents,and simply explain the main core idea of these contents.Chapter 2: Based on Bernstein operator,a new type of Beta operator with parameters is constructed.The parameters belong to real numbers and are greater than zero.On this basis,we take a Korovkin type approximation theorem as the research object,and construct a local approximation theorem based on it,and prove the function of Lipschitz’s continuous convergence theorem.At the same time,we receive a Voronovskaja type asymptotic formula,which further generalizes the Bernstein operator and lays a theoretical basis for follow-up work of the Beta basis function model.Chapter 3: Based on the Bernstein basis function model,a beta basis function model with parameters is proposed.The trend of the curve could be affected by changing the shape parameter value of the beta basis function model.When the shape parameter is adjusted,the fitting accuracy of this model is amazing and has the same fitting effect as the Bernstein basis function model.The Bernstein basis function model is extended and improved through the Beta basis function model,which is more flexible,which provides a new idea for further research on data mining models.Chapter 4: Make a summary of the contents stated in the full text,and at the same time make a more specific outlook for the research of Beta operators in the field of approximation theory and Beta basis functions in the field of data mining.