半变系数模型平均的权重估计研究  

Weight Estimation of Varying-coefficient Semiparametric Model Averaging

作　　者：薛婷 谭安琪 李维萍 黄磊[1] XUE Ting;TAN Anqi;LI Weiping;HUANG Lei(College of Mathematics,Southwest Jiaotong University,Chengdu Sichuan 611730,China;College of Finance and Statistics,Hunan University,Changsha Hunan 410006,China)

机构地区：[1]西南交通大学数学学院,成都611730 [2]湖南大学金融与统计学院,长沙410006

出　　处：《西华师范大学学报（自然科学版）》2020年第3期295-301,共7页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金青年科学基金项目(11601147)。

摘　　要：预测是重要的统计学数据分析任务之一,广泛运用的参数模型对数据的分布以及数据之间的相互关系有较强的假设,而非参数模型在涉及多维解释变量时会因维度灾难而导致模型的估计和预测效果都不理想。因此,本文将运用一种新的变系数半参数模型平均预测(VC-SMAP)的方法来进行预测,并且提出一种改进的确定模型权重的研究思路,即首先用训练集来估计模型参数,再用验证集来估计模型权重,最后用测试集来判断预测效果,其中运用了样条估计方法对半变系数模型进行参数估计,并用二次规划估计了模型权重。此外,还通过数值模拟的例子来展示所提方法的改进效果。另外还进行了实证分析,其结果也表明所提出的研究思路可行且更有效。Prediction is one of the fundamental tasks in statistical analysis.Parametric model has strong assumptions on the distribution of data and the relationship between the data while the estimation and prediction efficiency of non-parametric model is not so desirable due to "curse of dimensionality" as the number of covariates grows.Therefore,this paper introduces a new method called varying-coefficient semiparametric model averaging prediction(VC-SMAP) and proposes a novel approach to determine the model weights.Firstly,the model parameters are estimated by training set.Then,the weights of the model is estimated by validation set.Finally,the prediction effect is examined by test set.Moreover,Spline approximation is used for the estimation of varying-coefficients parameters and model weights are estimated by quadratic programming.In addition,the performance of the proposed method is investigated through statistical simulations.The results of empirical analysis also demonstrates its feasibility and better accuracy.

关 键 词：半变系数模型 模型平均 样本外预测 样条估计 二次规划 

分 类 号：C81[社会学—统计学]