Semiparametric Regression Analysis With Missing Response at Random
响应随机缺失时的半参数回归分析AI 解读 ↓
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响应随机缺失时的半参数回归分析
- 研究问题
- 在响应变量随机缺失的半参数部分线性回归中，如何构造估计与置信区间，并缓解非参数方法的维数困难？
- 方法与思路
- 作者统一回归插补、边际平均和倾向得分加权估计，采用 jackknife 估计方差，并构造调整及 bootstrap 经验似然推断。
- 材料陈述的贡献
- 摘要称，该类估计渐近正态，三个特例具有相同渐近方差，并在同方差高斯情形达到半参数效率界；另给出经验似然校正。
- 阅读关注点
- 应核对缺失机制、估计目标和非参数部分的条件，区分效率界适用情形，并比较不同区间方法的覆盖率与平均长度。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要，缺失机制细节和模拟数值未提供；效率结论有明确情形限制，倾向得分加权不自动赋予因果解释。
原文摘要
We develop inference tools in a semiparametric partially linear regression model with missing response data. A class of estimators is defined that includes as special cases a semiparametric regression imputation estimator, a marginal average estimator, and a (marginal) propensity score weighted estimator. We show that any of our class of estimators is asymptotically normal. The three special estimators have the same asymptotic variance. They achieve the semiparametric efficiency bound in the homoscedastic Gaussian case. We show that the jackknife method can be used to consistently estimate the asymptotic variance. Our model and estimators are defined with a view to avoid the curse of dimensionality, which severely limits the applicability of existing methods. The empirical likelihood method is developed. It is shown that when missing responses are imputed using the semiparametric regression method the empirical log-likelihood is asymptotically a scaled chi-squared variable. An adjusted empirical log-likelihood ratio, which is asymptotically standard chisquared, is obtained. Also, a bootstrap empirical log-likelihood ratio is derived and its distribution is used to approximate that of the imputed empirical log-likelihood ratio. A simulation study is conducted to compare the adjusted and bootstrap empirical likelihood with the normal approximation-based method in terms of coverage accuracies and average lengths of confidence intervals. Based on biases and standard errors, a comparison is also made by simulation between the proposed estimators and the related estimators.