Asymptotic properties of Lasso in high-dimensional partially linear models

Chi Ma, Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)769-788
Number of pages20
JournalScience China Mathematics
Volume59
Issue number4
DOIs
Publication statusPublished - 1 Apr 2016
Externally publishedYes

Keywords

  • irrepresentable condition
  • Lasso
  • restricted eigenvalue
  • semiparametric models
  • sparsity

ASJC Scopus subject areas

  • Mathematics(all)

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