Testing the linearity in partially linear models

Abstract

A test is proposed to check the linearity of the nonparametric portion in the partially linear regression model with a linear interpolation. The test is given by a p-value which is derived using the fiducial method. This p-value can also be thought as a generalised p-value. Under the null hypothesis, the p-value is uniformly distributed on interval (0, 1). Meanwhile the test is consistent under mild conditions. Finally, a good finite sample performance of the test is investigated by simulations, in which comparisons with other tests are also given.

Keywords:

• correct level
• fiducial inference
• p-value
• partially linear model
• testing linearity

Acknowledgements

We are grateful to the referees and an Associate Editor for very constructive comments on an earlier version of this paper.

Notes

^†This work is supported by Chinese National Natural Science Foundation with grant No. 10771015.