Functional kernel-weighted least square estimation and its applications in economics

TU Yundong, WANG Siwei

Systems Engineering - Theory & Practice ›› 2019, Vol. 39 ›› Issue (4) : 839-853.

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Systems Engineering - Theory & Practice ›› 2019, Vol. 39 ›› Issue (4) : 839-853. DOI: 10.12011/1000-6788-2018-2000-15

Functional kernel-weighted least square estimation and its applications in economics

  • TU Yundong1,2,3, WANG Siwei1
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Abstract

In this article, we propose a new method called functional kernel-weighted least squares (FKLS) method to estimate the smooth coefficient function in semi-parametric smooth coefficient model. This novel proposal ingeniously combines the kernel-weighted least squares (KLS) and the functional least squares (FLS) methods. The corresponding FKLS estimator is defined based on the loss function constructed by the conditional characteristic function. It not only has the advantage of FLS method that can produce robust parameter estimation even if the disturbance is subject to heavy tailed distributions, but also has the characteristics of non-parametric kernel estimation that consistency can be achieved without the knowledge of the correct functional form. The consistency and asymptotic normality of the proposed estimator are established. Furthermore, adaptive estimation is investigated based on the consistent estimator of the asymptotic variance. Finally, superiority of the FKLS estimator in finite samples, compared to the KLS estimator, is demonstrated through simulated numerical examples and the study of PM2.5 and economic growth in China.

Key words

adaptive estimation / environmental Kutznets curve / functional coefficient model / functional least squares / heavy tailed distribution / kernel estimation

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TU Yundong , WANG Siwei. Functional kernel-weighted least square estimation and its applications in economics. Systems Engineering - Theory & Practice, 2019, 39(4): 839-853 https://doi.org/10.12011/1000-6788-2018-2000-15

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Funding

National Natural Science Foundation of China (71472007, 71532001, 71671002); National Key Research and Development Program of China (2016YFC0207705)
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