In this chapter 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 (SIMs) 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 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 SIM, 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 (IMSE) than SIM-Lasso.
The authors are thankful to the co-editors and two anonymous referees for helpful comments, and the seminar participants at the Advances in Econometrics conference at the University of California, Irvine.
Chu, J., Lee, T. and Ullah, A. (2019), "Variable Selection in Sparse Semiparametric Single Index Models", Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part B (Advances in Econometrics, Vol. 40B), Emerald Publishing Limited, pp. 65-88. https://doi.org/10.1108/S0731-90532019000040B005Download as .RIS
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