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Estimation and testing for panel data partially linear single-index models with errors correlated in space and time
Random Matrices: Theory and Applications ( IF 0.9 ) Pub Date : 2019-09-27 , DOI: 10.1142/s2010326321500052
Jian-Qiang Zhao 1 , Yan-Yong Zhao 2 , Jin-Guan Lin 2 , Zhang-Xiao Miao 1 , Waled Khaled 3
Affiliation  

We consider a panel data partially linear single-index models (PDPLSIM) with errors correlated in space and time. A serially correlated error structure is adopted for the correlation in time. We propose using a semiparametric minimum average variance estimation (SMAVE) to obtain estimators for both the parameters and unknown link function. We not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. Then, a fitting of spatial and time-wise correlation structures is investigated. Based on the estimators, we propose a generalized F-type test method to deal with testing problems of index parameters of PDPLSIM with errors correlated in space and time. It is shown that under the null hypothesis, the proposed test statistic follows asymptotically a [Formula: see text]-distribution with the scale constant and degrees of freedom being independent of nuisance parameters or functions. Simulated studies and real data examples have been used to illustrate our proposed methodology.

中文翻译:

误差在空间和时间上相关的面板数据部分线性单指标模型的估计与检验

我们考虑在空间和时间上具有相关误差的面板数据部分线性单指数模型 (PDPLSIM)。时间相关采用序列相关误差结构。我们建议使用半参数最小平均方差估计 (SMAVE) 来获得参数和未知链接函数的估计量。我们不仅为单个指标中的参数估计量和模型的线性分量建立了渐近正态分布,而且得到了未知链接函数的非参数局部线性估计量的渐近正态分布。然后,研究了空间和时间相关结构的拟合。基于估计器,我们提出了一种广义的F型测试方法来处理PDPLSIM的指标参数在空间和时间上相关的误差的测试问题。结果表明,在原假设下,所提出的检验统计量渐近地遵循 [公式:参见文本]-分布,其中尺度常数和自由度独立于有害参数或函数。模拟研究和真实数据示例已用于说明我们提出的方法。
更新日期:2019-09-27
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