Approximation Properties Of Modified Two-parameter Bernstein Basis Functions And Their Application In Statistical Prediction

With the development and progress of society,the q calculus has been widely used in the field of probability operators.In particular,the classic Bernstein operator has attracted the attention of many scholars because of its excellent properties,which makes its research field increasingly rich.Its basis function is one of the important tools for curve design.This dissertation proposes modified(λ,q)-Bernstein-Kantorovich operator,and the basis function fitting prediction model is improved by combining numerical calculation and some parametric optimization algorithms,and then we conclude into five parts.Firstly,we introduce the factors affecting crude oil price,the influence of fuel oil price on the economy and industry,the research status of fuel oil price fitting forecast at home and abroad,and some theories and methods commonly used in the forecast.Secondly,we construct a class of modified(λ,q)-Bernstein-Kantorovich operators.First of all,the origin moment and central moment of the operator are calculated,then the local approximation property is studied according to the definition of K-functional and the first and second order optical sliding modes,and then the point estimation is carried out according to the property of Lipschitz function class.Finally,some approximation results of the operator in weighted space are studied.Thirdly,we set up a modified two-parameter Bernstein basis function fitting prediction model.Based on the least square regression,the ridge regression was introduced to estimate the control points,and the model parameters were optimized by combining the PSO algorithm and the grid search method.Then,the adjusted determination coefficient was taken as the evaluation index,and the optimal shape parameters,ridge parameters and the number of control points were obtained by matlab simulation.The research results of traditional Bernstein basis function fitting prediction model are extended.Fourthly,we analyze the empirical results of the modified two-parameter Bernstein basis function fitting prediction model,and the results show that the flexibility and accuracy of the proposed model are better than the traditional Bernstein basis function model.Fifthly,we summarize the content of the dissertation and puts forward a further prospect for the optimization of the basis function fitting prediction model.In this dissertation,we combine the new basis function with the intelligent algorithm and proves that the fitting prediction effect of the combined model is very significant through the example.The new basis function improves the fitting accuracy of the model and the complexity of the estimation.The optimized parameter estimation method can make up for the shortcomings of the former.Therefore,the combination of various technologies has a very broad development prospect.