Doubly robust and efficient estimators for heteroscedastic partially linear single-index models allowing high dimensional covariates.
Doubly robust and efficient estimators for heteroscedastic partially linear single-index models allowing high dimensional covariates.
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DOI：
10.1111/j.1467-9868.2012.01040.x
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发表时间：
2013-03
期刊：
影响因子：
--
通讯作者：
Zhu L
中科院分区：
文献类型：
--
作者：
Ma Y;Zhu L
我们研究具有未指定误差方差函数的异方差部分线性单指数模型，该模型允许均值函数的线性和单指数分量中存在高维协变量。我们通过使用适当的加权策略提出了一类参数的一致估计器。一个有趣的发现是，降维文献中广泛假设的线性条件对于方法论或理论发展来说并不是必需的：它仅有助于简化非最优一致估计。我们还发现，当非参数分量估计错误时，通常的加权最小二乘类型估计器的性能会恶化。然而，我们家族中的估计器会自动提供防止这种恶化的保护，因为即使基线非参数函数完全错误指定，也可以实现一致性。我们进一步表明，最有效的估计量是该家族的成员，并且可以通过使用非参数估计轻松获得。通过理论说明和数值模拟展示了所提出的估计量的特性。使用性别歧视的例子来展示和比较估计者的实际表现。
We study the heteroscedastic partially linear single-index model with an unspecified error variance function, which allows for high dimensional covariates in both the linear and the single-index components of the mean function. We propose a class of consistent estimators of the parameters by using a proper weighting strategy. An interesting finding is that the linearity condition which is widely assumed in the dimension reduction literature is not necessary for methodological or theoretical development: it contributes only to the simplification of non-optimal consistent estimation. We also find that the performance of the usual weighted least square type of estimators deteriorates when the non-parametric component is badly estimated. However, estimators in our family automatically provide protection against such deterioration, in that the consistency can be achieved even if the baseline non-parametric function is completely misspecified. We further show that the most efficient estimator is a member of this family and can be easily obtained by using non-parametric estimation. Properties of the estimators proposed are presented through theoretical illustration and numerical simulations. An example on gender discrimination is used to demonstrate and to compare the practical performance of the estimators.
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影响因子：
4.5
作者：
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通讯作者：
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DOI：
10.1111/j.1467-9868.2005.00533.x
发表时间：
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影响因子：
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