线性测量误差模型的平均估计

FREQUENTIST MODEL AVERAGE ESTIMATION FOR LINEAR ERRORS-IN-VARIABLES MODELS

频率模型平均估计近年来受到了较大的关注,但对有测量误差的观测数据尚未见到任何研究.文章主要考虑了线性测量误差模型的平均估计问题,导出了模型平均估计的渐近分布,基于Hjort和Claeskens(2003)的思想构造了一个覆盖真实参数的概率趋于预定水平的置信区间,并证明了该置信区间与基于全模型正态逼近所构造的置信区间的渐近等价性.模拟结果表明当协变量存在测量误差时,模型平均估计能明显增加点估计的效率.

Frequentist model average estimation receives much attention in recent years. However,no investigation has been conducted for the data with measurement errors.In this paper,we consider frequentist model average estimation for linear errors-in-variables models. The asymptotic distribution of the model average estimator is derived,and a confidence interval having a coverage probability that tends toward the nominal level in large samples is constructed.Further,the confidence interval constructed based on the model average estimator is shown to be asymptotically the same as that obtained under the full model.A simulation study shows that the finite sample performance of the model average estimator is better than that of the model selection approach or of the full model approach.