局部平稳部分线性面板数据模型的统计推断

Statistical Inference for Locally Stationary Partially Linear Panel Data Models

部分线性模型是一类非常重要的半参数回归模型,由于它既含有参数部分又含有非参数部分,与常规的线性模型相比具有更强的适应性和解释能力。文章研究带有局部平稳协变量的固定效应部分线性面板数据模型的统计推断。首先提出一个两阶段估计方法得到模型中未知参数和非参数函数的估计,并证明估计量的渐近性质,然后运用不变原理构造出非参数函数的一致置信带,最后通过数值模拟研究和实例分析验证了该方法的有效性。

Partially linear model is a very important semi-parametric regression model. Since the model contains both the parametric part and the non-parametric part, it has stronger adaptability and interpretability than common liner models. This paper studies the statistical inference for a fixed effect partially linear panel data model with locally stationary covariates. Firstly, a two-stage estimation method is proposed to estimate the unknown parameters and non-parametric functions in the model, and the asymptotic properties of the estimators are proved. Then the uniform confidence band of non-parametric functions is constructed by using the invariance principle. Finally, the effectiveness of the proposed method is verified by numerical simulation and example analysis.