响应变量缺失下部分线性单指标模型的经验似然推断

Empirical Likelihood Inference for Partially Linear Single-Index Models with Missing Responses

摘要: 本文研究响应变量随机缺失下部分线性单指标模型的经验似然推断问题。首先，基于响应变量随机缺失机制，分别采用逆概率加权方法和增广借补方法，构造了两类纠偏的参数向量的经验对数似然比统计量。然后，在适当的正则条件下，证明了上述两类统计量均渐近服从标准卡方分布，进而建立了参数向量的经验似然置信域。最后，给出了参数向量的极大经验似然估计量和链接函数估计量的渐近分布。Monte Carlo模拟研究表明，与逆概率加权经验似然方法相比，增广借补经验似然方法在有限样本条件下表现更好。

Abstract: This paper investigates empirical likelihood inference for partially linear single-index models with randomly missing response variables. First, under the missing-at-random mechanism, two types of bias-corrected empirical log-likelihood ratio statistics for the parameter vector are constructed based on the inverse probability weighting method and the augmented imputation method, respectively. Then, under appropriate regularity conditions, it is shown that both types of statistics asymptotically follow the standard chi-square distribution, and consequently empirical likelihood confidence regions for the parameter vector are established. Finally, the asymptotic distributions of the maximum empirical likelihood estimator of the parameter vector and the estimator of the link function are derived. Monte Carlo simulation studies indicate that, compared with the inverse probability weighting empirical likelihood method, the augmented imputation empirical likelihood method performs better in finite samples.