Variable Selection for Panel Data Linear Regression Models with Fixed Effects

Xinye Hui

doi:10.62051/ijsspa.v2n2.17

Authors

Xinye Hui

DOI:

https://doi.org/10.62051/ijsspa.v2n2.17

Keywords:

Compound Quantile Regression, MIXED Penalty, Fixed Effects, Variable Selection

Abstract

This paper introduces a robust variable selection mechanism for fixed effect panel data models by integrating compound quantile regression with the adjusted MIXED penalty method. Initially, forward orthogonal deviation transformation is employed to eliminate the influence of fixed effects. Subsequently, the MIXED penalty is utilized to construct a penalized compound quantile regression objective function, facilitating simultaneous estimation of regression coefficients and variable selection. This method not only effectively eliminates the interference of fixed effects but also demonstrates outstanding robustness. Its performance with limited sample sizes was validated through simulation studies, and its practical value was illustrated through application in real data analysis.

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References

Kock , B. (2013).Oracle efficient variable selection in random and fixed effects panel data models. Econometric Theory, 29(1), 115-152. https://doi.org/10.1017/S0266466612000230.

Kock ,B. Tang , H. (2019).Uniform inference in high-dimensional dynamic panel data models with approximately sparse fixed effects. Econometric Theory,,35(2), 295-359. https://doi.org/10.48550/arXiv.1501.00478.

Li ,Y., Zeng, X .B. (2014).Research on the penalized likelihood variable selection method for panel data models. Statistical Research, 31(03), 83-89. https://doi.org/10.19343/j.cnki.11-1302/c.2014.03.012.

Tang, L. Z., Li Y. J., Zhao L J. (2020).Research on the Bayesian Elastic Net quantile regression method for panel data and its application. Statistical Research , 37(03),94-113. https://doi.org/10.19343/j.cnki.11-1302/c.2020.03.008.

Lv, Y. Z., Zhang, R. Q., Zhao, W. H., Liu, J. C. (2014). Composite Quantile Regression and Variable Selection for Partial Linear Single-Index Models. Scientia Sinica Mathematica, 44(12), 1299-1322.

Wang, K. N., Li, S. M., Lin, L. (2020). Composite Quantile Regression and Variable Selection for Longitudinal Data Based on the Copula Function. Scientia Sinica Mathematica, 50(8), 1097-1116.

Weng, Y. L., Yu, P., Zhang, Z. Z. (2019). Composite Quantile Estimation for Functional Linear Models with Dependent Errors. Journal of Applied Probability and Statistics, 35(4), 360-372.

Wu, D. S., Yu, L., Yang, Y. P. (2019). The Impact of China's Foreign Trade on Economic Growth - Based on an Improved Two-Stage Panel Data Quantile Regression. Journal of Mathematical Statistics and Management, 38(4), 571-579.

Liu, H. L. (2016). Studies on Statistical Models Based on Composite Quantile Regression Methods. Chongqing: Chongqing University.

Li, G. R., Lian, H., Lai, P., Peng, H. (2015). Variable Selection for Fixed Effects Varying Coefficient Models. Acta Mathematica Sinica (English Series), 31(1), 91-110. https://doi.org/10.1007/s10114-015-3159-2.

Wei, J. (2019). High-Dimensional Testing Research in Panel Data Models. China Economics Publishing House.

Gu, Z. T., Song, Z. F., Li, Y. (2020). Research on the Construction of Enhanced Index Funds Based on LASSO Variable Selection and Multifactor Models. Journal of Mathematical Statistics and Management, 39(3), 417-428. https://doi.org/10.13860/j.cnki.sltj.20200122-006.