Empirical likelihood-based inference in linear errors-in-covariables models with validation data
Empirical likelihood-based inference in linear errors-in-covariables models with validation data
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DOI：
10.1093/biomet/89.2.345
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发表时间：
2002-06-01
期刊：
影响因子：
2.7
通讯作者：
Rao, JNK
中科院分区：
文献类型：
--
作者：
Wang, QH;Rao, JNK
考虑线性误差协变量模型，假设除了响应变量和替代协变量的主要数据外，协变量的独立验证数据可用。我们首先开发了一个估计的经验对数似然的帮助下，验证数据，并证明其渐近分布是一个独立的标准卡（1）（2）随机变量的加权和未知的权重。通过一致地估计未知权重，我们构造了回归参数向量的估计经验似然置信区域。我们还提出了一个调整的经验对数似然，并证明其渐近分布是一个标准的卡方（2）。为了避免估计未知的权重或调整因子，我们提出了一个部分平滑的自助经验对数似然构造一个置信区域，具有渐近正确的覆盖概率。仿真研究进行比较所提出的方法与基于正态近似的方法的覆盖精度和置信区间的平均长度。
Linear errors-in-covariables models are considered, assuming the availability of independent validation data on the covariables in addition to primary data on the response variable and surrogate covariables. We first develop an estimated empirical loglikelihood with the help of validation data and prove that its asymptotic distribution is that of a weighted sum of independent standard chi(1)(2) random variables with unknown weights. By estimating the unknown weights consistently, we construct an estimated empirical likelihood confidence region for the regression parameter vector. We also suggest an adjusted empirical loglikelihood and prove that its asymptotic distribution is a standard chi(2). To avoid estimating the unknown weights or the adjustment factor, we propose a partially smoothed bootstrap empirical loglikelihood for constructing a confidence region which has asymptotically correct coverage probability. A simulation study is conducted to compare the proposed methods with a method based on a normal approximation in terms of coverage accuracy and average length of the confidence interval.