International journal of statistics and management system最新文献

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Inference for Seemingly Unrelated Varying-Coefficient Nonparametric Regression Models. 看似不相关的变化系数非参数回归模型的推断。

International journal of statistics and management system

Pub Date : 2010-01-01

Jinhong You, Haibo Zhou

This paper is concerned with the inference of seemingly unrelated (SU) varying-coefficient nonparametric regression models. We propose an estimation for the unknown coefficient functions, which is an extension of the two-stage procedure proposed by Linton, et al. (2004) in the longitudinal data framework where they focused on purely nonparametric regression. We show the resulted estimators are asymptotically normal and more efficient than those based on only the individual regression equation even when the error covariance matrix is homogeneous. Another focus of this paper is to extend the generalized likelihood ratio technique developed by Fan, Zhang and Zhang (2001) for testing the goodness of fit of models to the setting of SU regression. A wild block bootstrap based method is used to compute p-value of the test. Some simulation studies are given in support of the asymptotics. A real data set from an ongoing environmental epidemiologic study is used to illustrate the proposed procedures.

本文关注看似不相关（SU）变化系数非参数回归模型的推断。我们提出了一种未知系数函数的估计方法，这是对 Linton 等人（2004 年）在纵向数据框架下提出的两阶段程序的扩展，他们将重点放在纯非参数回归上。我们证明，即使误差协方差矩阵是同质的，所得到的估计值也是渐近正态的，而且比那些仅基于单个回归方程的估计值更有效。本文的另一个重点是将 Fan、Zhang 和 Zhang（2001 年）开发的用于测试模型拟合度的广义似然比技术扩展到 SU 回归的环境中。本文采用了一种基于野生区块引导的方法来计算检验的 p 值。为支持渐近论，还进行了一些模拟研究。一个正在进行的环境流行病学研究的真实数据集被用来说明所建议的程序。

引用次数: 0

Statistical Inference for Regression Models with Covariate Measurement Error and Auxiliary Information. 具有协变量测量误差和辅助信息的回归模型的统计推断。

International journal of statistics and management system

Pub Date : 2009-01-01

Jinhong You, Haibo Zhou

We consider statistical inference on a regression model in which some covariables are measured with errors together with an auxiliary variable. The proposed estimation for the regression coefficients is based on some estimating equations. This new method alleates some drawbacks of previously proposed estimations. This includes the requirment of undersmoothing the regressor functions over the auxiliary variable, the restriction on other covariables which can be observed exactly, among others. The large sample properties of the proposed estimator are established. We further propose a jackknife estimation, which consists of deleting one estimating equation (instead of one obervation) at a time. We show that the jackknife estimator of the regression coefficients and the estimating equations based estimator are asymptotically equivalent. Simulations show that the jackknife estimator has smaller biases when sample size is small or moderate. In addition, the jackknife estimation can also provide a consistent estimator of the asymptotic covariance matrix, which is robust to the heteroscedasticity. We illustrate these methods by applying them to a real data set from marketing science.

我们考虑一个回归模型的统计推断，其中一些协变量与辅助变量一起测量误差。本文提出的回归系数估计是基于一些估计方程。这种新方法减轻了以前提出的估计的一些缺点。这包括对辅助变量的回归函数进行欠平滑的要求，以及对可以精确观察到的其他协变量的限制等。建立了该估计量的大样本性质。我们进一步提出了一种折刀估计，它包括一次删除一个估计方程(而不是一个观测值)。证明了回归系数的折刀估计量与基于估计方程的估计量是渐近等价的。仿真结果表明，在样本大小较小或中等的情况下，叠刀估计具有较小的偏差。此外，刀切估计还能提供渐近协方差矩阵的一致估计量，对异方差具有较强的鲁棒性。我们通过将这些方法应用于营销科学的真实数据集来说明这些方法。

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