| 徐群芳,徐勤丰.半相依部分线性可加回归模型的统计推断[J].数学年刊A辑,2013,34(4):451~478 |
| 半相依部分线性可加回归模型的统计推断 |
| Statistical Inference of Seemingly Unrelated PartiallyLinear Additive Regression Models |
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| DOI： |
| 中文关键词: 半参数回归, 可加模型, 半相依模型, 级数逼近估计, 加权估计 |
| 英文关键词:Semiparametric regression, Additive models, Seemingly unrelated
regression models, Series/sieve estimation, Weighted estimation |
| 基金项目:国家自然科学基金 (No.11071154), 教育部人文与社会科学青年基金(No.10YJC910008)和上海财经大学创新基金 (No.CXJJ-2010-350 |
| Author Name | Affiliation | E-mail | | XU Qunfang | School of Statistics and Management, Shanghai University of Finance and Economics,
Shanghai 200433, China
School of Science, Zhejiang Agriculture and Forestry University, Lin'an 311300, Zhejiang, China. | tsunfangxu@163.com | | XU Qinfeng | Department of Statistics, School of Management, Fudan University, Shanghai 200433, China. | qfxu@fudan.edu.cn |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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