ABSTRACT This paper considers the shrinkage estimation of parameters of measurement error models when it is suspected that the parameters may belong to a linear subspace. The class of Liu type estimators is proposed by choosing five quasi-empirical Bayes estimators in the presence of measurement errors in the data. This class of estimator combines the sample and prior information together along with the good properties of ridge estimators and chosen five quasi-empirical Bayes estimators. The advantages of the proposed class of estimators over the classical ridge regression estimator is that the quasi-empirical Bayes estimators are a linear function of the tuning parameter. When data has problems of measurement errors and multicollinearity, then these estimators can handle both the issues simultaneously. The asymptotic properties of the estimators are derived and analyzed. A Monte Carlo simulation is conducted and its findings are reported.

中文翻译：

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测量误差模型中的刘型有偏估计量

摘要 当怀疑参数可能属于线性子空间时，本文考虑了测量误差模型参数的收缩估计。在数据中存在测量误差的情况下，通过选择五个准经验贝叶斯估计量，提出了 Liu 型估计量类。这类估计器结合了样本和先验信息以及岭估计器的良好特性，并选择了五个准经验贝叶斯估计器。所提出的一类估计量相对于经典岭回归估计量的优点在于准经验贝叶斯估计量是调整参数的线性函数。当数据存在测量误差和多重共线性问题时，这些估计器可以同时处理这两个问题。推导和分析估计量的渐近特性。进行蒙特卡罗模拟并报告其结果。