Estimation in a semiparametric partially linear errors-in-variables model
Estimation in a semiparametric partially linear errors-in-variables model
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DOI：
10.1214/aos/1017939140
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发表时间：
1999-10
影响因子：
4.5
通讯作者：
Hua Liang;W. Härdle;R. Carroll
中科院分区：
文献类型：
--
作者：
Hua Liang;W. Härdle;R. Carroll
我们考虑了当X以加性误差测量时，将响应Y与具有平均函数X T β + g(T)的预测因子（X， T）相关的部分线性模型。当忽略测量误差时，Severini和Staniswalis的半参数似然估计会导致参数β和函数g（.）的偏估计。我们推导了它们的估计量的一种简单修正，即衰减的通常参数修正的半参数版本。证明了β的估计量是相合的，并推导了其渐近分布理论。还开发了使用三明治式思想的一致标准误差估计。
We consider the partially linear model relating a response Y to predictors (X, T) with mean function X T β + g(T) when the X's are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswalis leads to biased estimates of both the parameter β and the function g(.) when measurement error is ignored. We derive a simple modification of their estimator which is a semiparametric version of the usual parametric correction for attenuation. The resulting estimator of β is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich-type ideas are also developed.