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针对所提出的具有可分时空过滤器的固定效应半参数单指标面板模型，本文构建模型未知参数和单指标函数的截面拟极大似然估计和检验模型非线性的F检验统计量，并从理论和模拟两方面分别考察估计量和检验统计量的大样本性质和有限样本表现。研究结果表明所构建的截面拟极大似然估计具有相合性和渐近正态性，F检验统计量渐近服从χ2分布；估计量和检验统计量具有良好的有限样本表现；忽略误差潜在的时空相关性会导致估计结果偏误较大，且有效性下降。本文还将所提出的模型估计技术和检验方法用于实证分析我国重工业碳排放强度的影响因素。
Abstract：For the proposed fixed effects semi-parametric single-index panel model with separable space-time filters, this paper constructs profile quasi-maximum likelihood estimators of unknown parameters and single-index function, and F-test statistic for testing the nonlinearity of the model. The large sample properties and finite sample performance of both the estimators and the test statistic are investigated in theory and simulation respectively. The research results show that: The constructed profile quasi-maximum likelihood estimators are consistent and asymptotically normal, and the F-test statistic follows a chi-square distribution asymptotically; The estimates and test statistic have good finite sample performance; Ignoring the potential space-time correlation of errors may lead to greater bias of the estimation results and reduce their effectiveness. In addition, we employ the proposed model estimation technique and testing method to empirically analyze the influencing factors of carbon emission intensity in Chinese heavy industry.
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(1)因篇幅所限，引理1~5与定理1~5的证明过程以附录1展示，见《统计研究》网站所列附件。下同。
(1)因篇幅所限，绘制单指标函数g(·)的拟合结果以附图1展示。
(2)因篇幅所限，模型（16）~(19)在相应参数设定下的参数估计结果以附表1和附表2展示。
(1)因篇幅所限，g(u)在不同r值下的轨迹图以附图2展示，不同显著水平τ下检验统计量的经验水平（r=0 ）和功效（r≠0 ）以附表3展示。
(2)因篇幅所限，各个协变量的非线性检验结果以附表4展示，LCI与各个协变量的散点图和拟合曲线以附图3展示。
(1)因篇幅所限，线性组合变量表示为0.1016LENSit+0.0867LFDIit+0.9852LPGDPit+0.0582LTECit+0.0899LIERit对碳排放强度的线性影响以附图4展示。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2026.03.010
中图分类号:O212.1
引用信息:
[1]陈建宝,李铂桂.具有可分时空过滤器的固定效应半参数单指标面板模型的估计和检验[J].统计研究,2026,43(03):134-146.DOI:10.19343/j.cnki.11-1302/c.2026.03.010.
基金信息:
国家社会科学基金一般项目“时空数据半参数回归模型的理论及其在我国区域经济领域的应用研究”（22BTJ024）
2025-04-24
2025
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