Research ArticleNo Access

Empirical likelihood for high-dimensional partially functional linear model

Zhiqiang Jiang

School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, P. R. China

Search for more papers by this author

Zhensheng Huang

School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, P. R. China

E-mail Address: stahzs@126.com

Corresponding author.

Search for more papers by this author

, and

Guoliang Fan

School of Economics and Management, Shanghai Maritime University, Shanghai 201306, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S2010326320500173Cited by:0 (Source: Crossref)

Abstract

This paper considers empirical likelihood inference for a high-dimensional partially functional linear model. An empirical log-likelihood ratio statistic is constructed for the regression coefficients of non-functional predictors and proved to be asymptotically normally distributed under some regularity conditions. Moreover, maximum empirical likelihood estimators of the regression coefficients of non-functional predictors are proposed and their asymptotic properties are obtained. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real data set is analyzed for illustration.

Keywords:

AMSC: 62G08, 62G20

References

1. G. Aneiros, R. Cao, R. Fraiman, C. Genest and P. Vieu, Recent advances in functional data analysis and high-dimensional statistics, J. Multivariate Anal. 170 (2019) 3–9. Crossref, Google Scholar
2. J. Chang, S. Chen and X. Chen, High dimensional generalized empirical likelihood for moment restrictions with dependent data, J. Econometric. 185 (2015) 283–304. Crossref, Google Scholar
3. B. Chen, G. Pan, Q. Yang and W. Zhou, Large dimensional empirical likelihood, Statist. Sinica 25 (2015) 1659–1677. Google Scholar
4. S. Chen, L. Peng and Y. Qin, Effects of data dimension on empirical likelihood, Biometrika 96 (2009) 711–722. Crossref, Google Scholar
5. F. Ferraty and P. Vieu, Nonparametric Functional Data Analysis: Theory and Practice (Springer, New York, 2006). Google Scholar
6. P. Hall and C. Hyde, Martingale Central Limit Theory and Its Application (Academic Press, New York, 1980). Google Scholar
7. Y. Hu, S. Feng and L. Xue, Empirical likelihood inference for partially functional linear model, Chin. J. Appl. Probability Statistic. 31 (2015) 146–158. Google Scholar
8. D. Kong, K. Xue, F. Yao and H. Zhang, Partially functional linear regression in high dimensions, Biometrika 103 (2016) 147–159. Crossref, Google Scholar
9. C. Lam and J. Fan, Profile-kernel likelihood inference with diverging number of parameters, Annal. statistic. 36 (2008) 2232–2260. Crossref, Google Scholar
10. C. Leng and C. Tang, Penalized empirical likelihood and growing dimensional general estimating equations, Biometrika 99 (2012) 703–716. Crossref, Google Scholar
11. G. Li, L. Lin and L. Zhu, Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters, J. Multivariate Anal. 105 (2012) 85–111. Crossref, Google Scholar
12. A. Owen, Empirical likelihood ratio confidence intervals for a single functional, Biometrika 75 (1988) 237–249. Crossref, Google Scholar
13. A. Owen, Empirical likelihood ratio confidence regions. Annal. Statistic. 18 (1990) 90–120. Crossref, Google Scholar
14. A. Owen, Empirical Likelihood (Chapman and Hall, CRC, 2001). Crossref, Google Scholar
15. J. Ramsay and B. Silverman, Functional Data Analysis (Springer, New York, 1997). Crossref, Google Scholar
16. H. Shin, Partial functional linear regression, J. Statistic. Plann. Inferen. 139 (2009) 3405–3418. Crossref, Google Scholar
17. H. Shin and M. Lee, On prediction rate in partial functional linear regression, J. Multivariate Anal. 103 (2012) 93–106. Crossref, Google Scholar
18. A. Van der Vaart, Asymptotic Statistics (Cambridge University Press, 1998). Crossref, Google Scholar
19. Y. Xia and W. Härdle, Semi-parametric estimation of partially linear single-index models, J. Multivariate Anal. 97 (2006) 1162–1184. Crossref, Google Scholar
20. L. Xue and L. Zhu, Empirical Likelihood in Nonparametric and Semiparametric Models (Science Press, 2010). Google Scholar
21. P. Yu, Z. Zhang and J. Du, A test of linearity in partial functional linear regression, Metrika 79 (2016) 953–969. Crossref, Google Scholar
22. J. Zhang, H. Shi, L. Tian and F. Xiao, Penalized generalized empirical likelihood in high-dimensional weakly dependent data, J. Multivariate Anal. 171 (2019) 270–283. Crossref, Google Scholar
23. H. Zhu, R. Zhang, Z. Yu, H. Lian and Y. Liu, Estimation and testing for partially functional linear errors-in-variables models, J. Multivariate Anal. 170 (2019) 296–314. Crossref, Google Scholar