Maity Arnab, Apanasovich Tatiyana V
Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A.
Electron J Stat. 2011;5:1424-1449. doi: 10.1214/11-EJS647.
This paper considers the problem of estimation in a general semiparametric regression model when error-prone covariates are modeled parametrically while covariates measured without error are modeled nonparametrically. To account for the effects of measurement error, we apply a correction to a criterion function. The specific form of the correction proposed allows Monte Carlo simulations in problems for which the direct calculation of a corrected criterion is difficult. Therefore, in contrast to methods that require solving integral equations of possibly multiple dimensions, as in the case of multiple error-prone covariates, we propose methodology which offers a simple implementation. The resulting methods are functional, they make no assumptions about the distribution of the mismeasured covariates. We utilize profile kernel and backfitting estimation methods and derive the asymptotic distribution of the resulting estimators. Through numerical studies we demonstrate the applicability of proposed methods to Poisson, logistic and multivariate Gaussian partially linear models. We show that the performance of our methods is similar to a computationally demanding alternative. Finally, we demonstrate the practical value of our methods when applied to Nevada Test Site (NTS) Thyroid Disease Study data.
本文考虑了一般半参数回归模型中的估计问题，其中易出错的协变量采用参数化建模，而无误差测量的协变量采用非参数化建模。为了考虑测量误差的影响，我们对一个准则函数进行了修正。所提出的修正的具体形式允许在难以直接计算修正准则的问题中进行蒙特卡罗模拟。因此，与需要求解可能多维的积分方程的方法不同，如在多个易出错的协变量的情况下，我们提出了一种实现简单的方法。所得方法具有泛函性，它们对误测协变量的分布不做任何假设。我们利用轮廓核和反向拟合估计方法，并推导了所得估计量的渐近分布。通过数值研究，我们证明了所提出的方法在泊松、逻辑和多元高斯部分线性模型中的适用性。我们表明，我们方法的性能与一种计算要求较高的替代方法相似。最后，我们展示了我们的方法应用于内华达试验场（NTS）甲状腺疾病研究数据时的实用价值。
