存在潜在模型偏误时小域估计的不确定性评价:一带一路法  

Assessing uncertainty in small area estimation involving model misspecification:A one-bring-one route

作　　者：刘小惠[1] 马海强 蒋继明 Xiaohui Liu;Haiqiang Ma;Jiming Jiang

机构地区：[1]江西财经大学统计学院,南昌330013 [2]Department of Statistics,University of California at Davis,Davis,Davis95616UA

出　　处：《中国科学：数学》2022年第7期779-808,共30页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11971208,11601197,11701235和11961028);中国博士后基金(批准号:2016M600511和2017T100475);江西省自然科学基金(批准号:2018ACB21002,2017ACB21030和20171BAB211004);美国国家科学基金(批准号:DMS-1510219)资助项目。

摘　　要：当可能存在模型偏误时,现有结果表明小域估计中观测最佳预测比传统的经验最佳线性无偏预测的预测精度更高,表现更加稳健.然而,出于稳健性考虑,实际所用的假设模型无法直接用于推导观测最佳预测相关的均方预测误差的估计,从而导致其不确定性评价变得困难重重.有鉴于此,本文着重考虑观测最佳预测有关均方预测误差的估计问题,提出一类具有解析形式的针对无条件均方预测误差的估计,并在一定条件下推导出相关估计的二阶无偏性.模拟和实际数据例子均表明本文提出的新估计无论在理论方面还是在有限样本性质方面都有着比现有估计更好的表现.We consider the estimation of the mean squared prediction error(MSPE)for the observed best prediction(OBP)in the small area estimation(SAE)with potential model misspecification.Although the OBP has been shown to be more robust than the traditional empirical best linear unbiased prediction in terms of prediction accuracy under model misspecification,assessing uncertainty in OBP has been a difficult task due to the potential model misspecification.More specifically,the assumed model cannot be used in deriving an MSPE estimator in order to achieve robustness.We propose a method of deriving an analytic and second-order unbiased estimator of the unconditional MSPE of OBP,i.e.,the one that takes into account the variability in both response and covariates,under reasonable weak assumptions.We prove the second-order unbiasedness of the proposed MSPE estimator,evaluate its finite-sample performance,and demonstrate its superiority over the existing methods both theoretically and empirically.

关 键 词：模型偏误 观测最佳预测 二阶无偏性 小域估计 稳定性 无条件均方预测误差 

分 类 号：O212.1[理学—概率论与数理统计]