Journal of Systems Science and Complexity

, Volume 30, Issue 5, pp 1206–1226 | Cite as

Generalized F-test for high dimensional regression coefficients of partially linear models

  • Siyang Wang
  • Hengjian CuiEmail author


This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown nonlinear component by some nonparametric methods and then generalize the F-statistic to test the regression coefficients under some regular conditions. During this procedure, the estimation of the nonlinear component brings much challenge to explore the properties of generalized F-test. The authors obtain some asymptotic properties of the generalized F-test in more general cases, including the asymptotic normality and the power of this test with p/n ∈ (0, 1) without normality assumption. The asymptotic result is general and by adding some constraint conditions we can obtain the similar conclusions in high dimensional linear models. Through simulation studies, the authors demonstrate good finite-sample performance of the proposed test in comparison with the theoretical results. The practical utility of our method is illustrated by a real data example.


Generalized F-test high dimensional regression partially linear models power of test 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Statistics and MathematicsCentral University of Finance and EconomicsBeijingChina
  2. 2.School of Mathematical SciencesCapital Normal UniversityBeijingChina

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