High dimensional single index models

Peter Radchenko

Journal of Multivariate Analysis, 2015, vol. 139, issue C, 266-282

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.

Keywords: Nonlinear regression; High-dimensional data; Single index model; Sparsity; Regularization (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:139:y:2015:i:c:p:266-282

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DOI: 10.1016/j.jmva.2015.02.007

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