Variable Selection in Sparse Semiparametric Single Index Models

Tae Hwy Lee, Jianghao Chu () and Aman Ullah
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Jianghao Chu: UCR

No 201908, Working Papers from University of California at Riverside, Department of Economics

Abstract: In this paper we consider the "Regularization of Derivative Expectation Operator" (Rodeo) of Lafferty and Wasserman (2008) and propose a modified Rodeo algorithm for semiparametric single index models in big data environment with many regressors. The method assumes sparsity that many of the regressors are irrelevant. It uses a greedy algorithm, in that, to estimate the semiparametric single index model (SIM) of Ichimura (1993), all coefficients of the regressors are initially set to start from near zero, then we test iteratively if the derivative of the regression function estimator with respect to each coefficient is significantly different from zero. The basic idea of the modified Rodeo algorithm for SIM (to be called SIM-Rodeo) is to view the local bandwidth selection as a variable selection scheme which amplifies the coefficients for relevant variables while keeping the coefficients of irrelevant variables relatively small or at the initial starting values near zero. For sparse semiparametric single index models, the SIM-Rodeo algorithm is shown to attain consistency in variable selection. In addition, the algorithm is fast to finish the greedy steps. We compare SIM-Rodeo with SIM-Lasso method in Zeng et al. (2012). Our simulation results demonstrate that the proposed SIM-Rodeo method is consistent for variable selection and show that it has smaller integrated mean squared errors than SIM-Lasso.

Keywords: Single index model (SIM); Variable selection; Rodeo; SIM-Rodeo; Lasso; SIM-Lasso. (search for similar items in EconPapers)
JEL-codes: C25 C44 C53 C55 (search for similar items in EconPapers)
Pages: 30 Pages
Date: 2018-09
New Economics Papers: this item is included in nep-big, nep-ecm and nep-ore
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https://economics.ucr.edu/repec/ucr/wpaper/201908.pdf First version, 2018 (application/pdf)

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Chapter: Variable Selection in Sparse Semiparametric Single Index Models (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:ucr:wpaper:201908

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