半相依部分线性可加回归模型的统计推断

受实际问题研究的启发, 为减少模型偏差, 提出了一类半相依部分线性可加的半参数回归模型. 这类半相依模型中, 响应变量与 一部分解释变量之间的关系是线性的, 与另一部分解释变量之间的关系未知但具有可加结构, 各方程的误差之间是相关的. 将级 数逼近法、最小二乘法和同期相关的估计结合起来, 提出了用于估计模型参数分量的加权半参数最小二乘估计量(WSLSEs), 和用于估 计模型非参数分量的加权级数逼近估计量(WSEs). 证明了这些加权的估计量比相应的不加权的估计量渐近有效, 并导出了相应的渐近正态性. 另外, 还讨论了利用这些估计量的渐近性质来对模型的参数及非参数分量作统计推断. 用大量的模拟实验考察 了所提出的方法在有限样本情况下的表现, 并对美国的一个关于妇女工资问题的全国纵向调查(NLS)数据集进行了统计分析.

Statistical Inference of Seemingly Unrelated Partially Linear Additive Regression Models

Motivated by an application and in order to reduce the modeling bias, the authors propose a class of semiparametric seemingly unrelated partially linear additive regression models, in which the relationship between the response and some covariates is linear, the relationship between the response and other covariates is allowed to be unknown and have an additive structure, and the errors are correlated across the equations. By combining the series/sieve approximation, least squares and estimating the contemporaneous correlation, the authors present a class of weighted semiparametric least squares estimators (WSLSEs for short) for the parametric components and a class of weighted series/sieve estimators (WSEs for short) for the nonparametric components. It is shown that these weighted estimators are asymptotically more efficient than the unweighted ones. Their asymptotic normalities are established. In addition, using these asymptotic properties to make statistical inference for the parametric and nonparametric components is also considered. The proposed methods are evaluated by wide simulation studies and applied to a national longitudinal surveys (NLS for short) data set about the wage of women in the United States.