具有空间和时间相关误差的面板数据部分线性单指标模型的估计与检验

Pub Date : 2020-04-01 DOI:10.1142/s2010326321500052
Jian-Qiang Zhao, Yan-Yong Zhao, Jinguan Lin, Zhang-Xiao Miao, Waled Khaled
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引用次数: 1

摘要

我们考虑了一个具有空间和时间相关误差的面板数据部分线性单指标模型(PDPLSIM)。时间上的相关采用了一种序列相关的误差结构。我们提出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。我们不仅建立了单指标参数估计量和模型线性分量的渐近正态分布,而且得到了未知环节函数的非参数局部线性估计量的渐近正态分布。然后,研究了空间相关结构和时间相关结构的拟合。在估计量的基础上,提出了一种广义f型检验方法,用于处理具有空间和时间相关误差的PDPLSIM指标参数的检验问题。结果表明,在零假设下,所提出的检验统计量渐近地服从一个[公式:见文本]-分布,其尺度常数和自由度与干扰参数或函数无关。模拟研究和实际数据实例已被用来说明我们提出的方法。
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Estimation and testing for panel data partially linear single-index models with errors correlated in space and time
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.
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