模型偏差的统计分析

Statistical Analysis of Model Bias

由于建模中存在种种近似,所建平差模型(包括回归、拟合、滤波模型等)在理论上必然包含模型误差。基于单位权意义下的均方误差概念,讨论了模型偏差的含义以及模型偏差和模型误差的关系;同时给出了模型偏差的识别和估计方法。通过对模型误差统计问题的深入分析,进一步明确了平差模型的常用假设检验的意义。作为实际例子,非线性模型线性化是平差中常用的建模方式,对舍去二次项引起的模型误差对平差结果的影响进行了统计分析。

Due to various approximations existing in the process of creating models, model error is contained unavoidably in created adjustment models including regress, fitting and filter models theoretically. In this paper, the notion of mean square error of model bias on basis of unit weight, and the relation between model error and model bias were discussed. Identifying and estimating methods of model bias were given at the same time. By deeply analyzing statistic problem of model error, the meaning of widely used hypothesis test of adjustment model was much clearer. Being a practical example of model error, linearization of non-linear model, an usual method for creating model in adjustment, whose influence owing to deleting quadratic item over adjustment result was analyzed under statistics as well.