Journal article
Asymptotic properties of Lasso in high-dimensional partially linear models
Science China. Mathematics, Vol.59(4), pp.769-788
11/25/2015
DOI: 10.1007/s11425-015-5093-2
Abstract
We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size. We use truncated series expansion based on polynomial splines to approximate the nonparametric component in this model. Under a sparsity assumption on the regression coefficients of the linear component and some regularity conditions, we derive the oracle inequalities for the prediction risk and the estimation error. We also provide sufficient conditions under which the Lasso estimator is selection consistent for the variables in the linear part of the model. In addition, we derive the rate of convergence of the estimator of the nonparametric function. We conduct simulation studies to evaluate the finite sample performance of variable selection and nonparametric function estimation.
Details
- Title: Subtitle
- Asymptotic properties of Lasso in high-dimensional partially linear models
- Creators
- Chi Ma - Anhui University of Science and TechnologyJian Huang - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Science China. Mathematics, Vol.59(4), pp.769-788
- Publisher
- Science China Press
- DOI
- 10.1007/s11425-015-5093-2
- ISSN
- 1674-7283
- eISSN
- 1869-1862
- Language
- English
- Date published
- 11/25/2015
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257615502771
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