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High dimensional single index models

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  • Radchenko, Peter

Abstract

This paper addresses the problem of fitting nonlinear regression models in high-dimensional situations, where the number of predictors, p, is large relative to the number of observations, n. Most of the research in this area has been conducted under the assumption that the regression function has a simple additive structure. This paper focuses instead on single index models, which are becoming increasingly popular in many scientific fields including biostatistics, economics and financial econometrics. Novel methodology is presented for estimating high-dimensional single index models and simultaneously performing variable selection. A computationally efficient algorithm is provided for constructing a solution path. Asymptotic theory is developed for the proposed estimates of the regression function and the index coefficients in the high-dimensional setting. An investigation of the empirical performance on both simulated and real data demonstrates strong performance of the proposed approach.

Suggested Citation

  • Radchenko, Peter, 2015. "High dimensional single index models," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 266-282.
    • Handle: RePEc:eee:jmvana:v:139:y:2015:i:c:p:266-282
    DOI: 10.1016/j.jmva.2015.02.007
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    Cited by:

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    2. Zhong, Wei & Liu, Xi & Ma, Shuangge, 2018. "Variable selection and direction estimation for single-index models via DC-TGDR method," IRTG 1792 Discussion Papers 2018-050, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Pircalabelu, Eugen & Artemiou, Andreas, 2021. "Graph informed sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    4. Hyung Park & Thaddeus Tarpey & Eva Petkova & R. Todd Ogden, 2024. "A high-dimensional single-index regression for interactions between treatment and covariates," Statistical Papers, Springer, vol. 65(7), pages 4025-4056, September.
    5. He, Yong & Zhang, Xinsheng & Zhang, Liwen, 2018. "Variable selection for high dimensional Gaussian copula regression model: An adaptive hypothesis testing procedure," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 132-150.
    6. Tan, Xin & Zhan, Haoran & Qin, Xu, 2023. "Estimation of projection pursuit regression via alternating linearization," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    7. Tan, Xin Lu, 2019. "Optimal estimation of slope vector in high-dimensional linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 179-204.
    8. Rong Jiang & Mengxian Sun, 2022. "Single-index composite quantile regression for ultra-high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 443-460, June.
    9. Zijuan Chen & Suojin Wang, 2023. "Inferences for extended partially linear single-index models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 602-622, June.

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