基于λ-Bernstein基函数模型的拟合研究  

Research on fitting model based onλ-Bernstein basis function

作　　者：程文韬 沈苏琴 CHENG Wen-tao;SHEN Su-qin(School of Mathematics and Physics,Anqing Normal University,Anqing 246000,Anhui,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246000

出　　处：《宝鸡文理学院学报（自然科学版）》2023年第4期10-14,共5页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金项目(11626031);安徽省自然科学基金项目(1908085QA29);安徽省高校自然科学研究重点项目(KJ2021A0648)。

摘　　要：目的推广传统的Bernstein基函数模型。方法选取2011-2022年燃料油期货收盘价格数据建立λ-Bernstein(广义Bernstein)基函数模型,结合最小二乘法和改进后的岭回归对参数进行估计,并以拟合精度为评价标准,通过调整模型参数λ的大小,选取合适的岭参数k,用MATLAB模拟调试得到最优的控制点个数m。结果与结论λ-Bernstein基函数模型的灵活性和拟合精度均高于传统的Bernstein基函数模型,λ-Bernstein基函数模型的拟合效果更优。Purposes—To extend the traditional Bernstein basis function model.Methods—The paper selected the data of the closing price of fuel oil futures from 2011 to 2022 to establishλ-Bernstein(generalized Bernstein)basis function model,combined with the least square method and the improved Ridge regression to estimate the parameters,and took the fitting accuracy as the evaluation standard,by adjusting the size of the model parameters,The optimal number of control points is obtained by selecting the appropriate ridge parameters and using MATLAB simulation debugging.Results and Conclusions—The flexibility and fitting accuracy of theλ-Bernstein basis function model are higher than that of the traditional Bernstein basis function model,theλ-Bernstein basis function model has better fitting effect.

关 键 词：λ-Bernstein基函数 控制点 岭回归 拟合 

分 类 号：O212.1[理学—概率论与数理统计]