Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters
Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters
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DOI：
10.1016/j.jmva.2011.08.010
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发表时间：
2012-02
期刊：
影响因子：
--
通讯作者：
Gaorong Li;Lu Lin;Lixing Zhu
中科院分区：
文献类型：
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作者：
Gaorong Li;Lu Lin;Lixing Zhu
本文的目的是双重的。首先，对于半参数模型中感兴趣的参数的估计或推断，通常使用的无限维干扰参数的插件估计会产生不可忽略的偏差，并且在文献中普遍采用最不利曲线或欠平滑来减少偏差。为了避免这种对模型的强结构假设和估计实现的不便，对于变系数部分线性模型中参数数量的发散，本文采用了偏校正经验似然（BCEL）。这种方法使得经验似然比的分布是渐近可处理的。然后可以直接应用它来构造感兴趣参数的置信区域。其次，与现有的所有方法不同，当样本数量趋于无穷大时，参数的发散数趋于无穷大时，我们对估计的一致性施加了强条件，以确保估计的一致性，我们提供的技术表明，除了通常的正则性条件外，仅在矩条件下，协变量和误差的一致性保持，发散速度比文献中更快。仿真研究了该方法的性能，并将其与轮廓最小二乘法进行了比较。为了说明这一点，本文分析了一个真实数据集。
The purpose of this paper is two-fold. First, for the estimation or inference about the parameters of interest in semiparametric models, the commonly used plug-in estimation for infinite-dimensional nuisance parameter creates non-negligible bias, and the least favorable curve or under-smoothing is popularly employed for bias reduction in the literature. To avoid such strong structure assumptions on the models and inconvenience of estimation implementation, for the diverging number of parameters in a varying coefficient partially linear model, we adopt a bias-corrected empirical likelihood (BCEL) in this paper. This method results in the distribution of the empirical likelihood ratio to be asymptotically tractable. It can then be directly applied to construct confidence region for the parameters of interest. Second, different from all existing methods that impose strong conditions to ensure consistency of estimation when diverging the number of the parameters goes to infinity as the sample size goes to infinity, we provide techniques to show that, other than the usual regularity conditions, the consistency holds under moment conditions alone on the covariates and error with a diverging rate being even faster than those in the literature. A simulation study is carried out to assess the performance of the proposed method and to compare it with the profile least squares method. A real dataset is analyzed for illustration.