摘要
当前整数值数据处理过程中,主要依靠连续型时间序列模型进行统计推断,操作过程中只能刻画数据线性特征,使得推断结果的标准化Pearson(皮尔森)残差较大。因此,文章提出基于空间自回归模型和最大似然估计的非线性整数值统计推断方法。应用H-RITNN(混合型鲁棒输入训练神经网络)非线性数据校正框架,将历史数据输入网络中,按照误差反传梯度下降法进行不断训练,找到异常数据并计算出校正值,完成观测样本数据预处理。利用给出数据样本建立残差空间自回归模型,描述数据包含的线性、非线性变化特点,并应用结合改进蚁群优化算法的最大似然估计算法求出模型未知参数,更新数据空间关系。以空间自回归模型为主,基于灰色理论的GM(1,1)模型和BP神经网络为辅,生成统计推断组合架构,基于此获取所需的非线性整数值。实验结果表明,新研究方法应用后给出的非线性整数值统计推断结果,标准化Pearson残差均值仅为0.02,证明其得出结果符合真实情况。
Current statistical inference for integer-valued data primarily relies on continuous time series models,which can only capture linear characteristics of the data during operation,leading to large standardized Pearson residuals in inference results.To address this issue,a nonlinear integer-valued statistical inference method based on a spatial autoregressive model and maximum likelihood estimation is proposed.First,a hybrid robust input training neural network(H-RITNN)nonlinear data correction framework is used.Historical data are input into the network and iteratively trained via the error backpropagation gradient descent algorithm to identify outliers and compute correction values,thereby completing the preprocessing of observed sample data.Next,a residual spatial autoregressive model is established using the given data samples to describe both linear and nonlinear variations in the data.The maximum likelihood estimation algorithm integrated with an improved ant colony optimization algorithm is employed to solve the unknown parameters of the model and update spatial relationships among the data.Finally,a composite statistical inference framework is constructed,with the spatial autoregressive model as the core component and the grey theory-based GM(1,1)model and BP neural network as supplementary components,to derive the required nonlinear integer values.Experimental results demonstrate that the proposed method achieves a mean standardized Pearson residual of only 0.02,confirming the validity of the inference results.
作者
刘苏兵
尤游
LIU Subing;YOU You(Public Basic Teaching Department,Anhui Mechanical and Electrical Vocational Technical College,Wuhu Anhui 241002,China;School of Mathematics-Physics and Finance,Anhui Polytechnic University,Wuhu Anhui 241000,China)
出处
《桂林航天工业学院学报》
2025年第3期423-432,共10页
Journal of Guilin University of Aerospace Technology
基金
安徽省教育厅质量工程课题项目“‘3+2’联合培养模式下本科层次职业教育数学课程衔接发展研究——以安徽机电职业技术学院为例”(2022JYXM261)
安徽省教育厅质量工程教学研究项目“(双高计划)背景下基于新工科建设和OBE理念的高等数学课程个性化教学研究”(2023jyxm1333)。
关键词
数据校正
空间自回归模型
最大似然估计
门限参数
整数值
统计推断
data correction
spatial autoregressive model
maximum likelihood estimation
threshold parameter
integer value
statistical inference
作者简介
刘苏兵,男,安徽滁州人。副教授,硕士。研究方向:数学教育、应用数学、经济统计等。
