基于SPSRs准则下的分类混合模型预测方法研究

The Study of Classified Mixed Model Prediction Method Based on SPSRs Rules

摘要: 分类混合模型预测(CMMP)方法是近年来小区域估计领域中提出的一种新方法，该方法是在待预测效应识别后的基础上形成的方法，较传统的混合效应预测方法有更高的预测精度，得到许多统计学者的关注。最早的分类混合模型预测方法是基于均方预测误差(MSPE)准则进行分类识别构造最佳预测。MSPE准则虽然是一个具有较好数学性质(对称性和平滑性)的不确定性度量准则，但是其不是一个严格适当的评分准则(SPSRs)。因此，提出了基于SPSRs准则(即对数评分)进行分类识别，构造最佳预测的方法。首先，在最佳预测的基础上构造了SPSRs分类器，并进行识别预测；其次分析了该预测的渐近性质，并通过数值模拟证明了该方法较经典的回归预测方法具有更高的准确度；最后，给出实例进一步论证了我们的理论结果。

Abstract: The Classified Mixed Model Prediction (CMMP) method is a newly proposed method in the field of small area estimation in recent years. The prediction accuracy of CMMP has attracted the attention of many statisticians. The earliest Classified Mixed Model Prediction is based on the Mean Square Prediction Error (MSPE) criterion for classification, identification and construction of the best pre-diction. Although the MSPE criterion is an uncertainty measurement criterion with good mathe-matical properties (symmetry and smoothness), it is not a Strictly Proper Scoring Rules (SPSRs). Therefore, we propose a method for classification and identification based on SPSRs criterion (i.e. logarithmic score) to construct the best prediction. Firstly, on the basis of the best prediction, the SPSRs classifier is constructed, identified and predicted. Secondly, the asymptotic properties of the prediction are analyzed, and the numerical simulation proves that this method has higher accuracy than the classical regression prediction method. Finally, an example is given to further demonstrate our theoretical results.