Semiparametric efficient estimation for partially linear single-index models with responses missing at random
Semiparametric efficient estimation for partially linear single-index models with responses missing at random
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DOI：
10.1016/j.jmva.2014.03.001
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发表时间：
2014-07
期刊：
影响因子：
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通讯作者：
Peng Lai;Qihua Wang
中科院分区：
文献类型：
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作者：
Peng Lai;Qihua Wang
本文建立了响应随机缺失的异方差部分线性单指标模型的半参数有效界，并给出了一种有效的估计方程方法。通过求解估计方程，我们同时得到了线性部分和单指标部分的参数向量的估计。当正确指定倾向得分函数时，估计量是渐近半参数有效的。应当注意，逆概率加权有效估计方程不能通过逆概率加权方法直接从全数据有效估计方程获得。通过推导观测数据的有效得分函数，建立了估计方程。一些模拟研究和真实的数据应用进行了评估和说明所提出的方法。
In this paper, we establish the semiparametric efficient bound for the heteroscedastic partially linear single-index model with responses missing at random, and develop an efficient estimating equation method. By solving the estimating equation, we obtain estimators for the parameter vectors in the linear part and the single index part simultaneously. The estimators are asymptotically semiparametrically efficient when the propensity score function is specified correctly. It should be noted that the inverse probability weighted efficient estimating equation cannot be obtained directly from the full data efficient estimating equation by the inverse probability weighted approach. We establish the estimating equation by deriving the observed data efficient score function. Some simulation studies and a real data application were conducted to evaluate and illustrate the proposed methods.