ABSTRACT For the high-dimensional partially linear errors-in-function model with martingale difference errors, we, in this paper, propose an empirical log-likelihood ratio function for the regression parameter. The empirical log-likelihood ratio is proven to be asymptotically chi-squared. In addition, we propose penalized empirical likelihood (PEL) for the parameter. By using an appropriate penalty function, we show that PEL has the oracle property. Also, we obtain the PEL ratio is defined and its limiting distribution is asymptotically chi-squared under the null hypothesis. Moreover, simulation studies and a real data example are undertaken to assess the finite sample performance of our proposed method.

中文翻译：

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带有马丁格尔差分误差的高维部分线性误差函数模型的惩罚经验似然

摘要 对于具有鞅差分误差的高维部分线性函数误差模型，我们在本文中提出了回归参数的经验对数似然比函数。经验对数似然比被证明是渐近卡方的。此外，我们为参数提出了惩罚经验似然（PEL）。通过使用适当的惩罚函数，我们证明 PEL 具有预言机属性。此外，我们获得了 PEL 比率的定义，其极限分布在零假设下渐近卡方。此外，还进行了模拟研究和真实数据示例，以评估我们提出的方法的有限样本性能。