Bootstrapping stochastic regression models under homoskedasticity: wild bootstrap vs. pairs bootstrap

Abstract

We investigate by simulation how the wild bootstrap and pairs bootstrap perform in t and F tests of regression parameters in the stochastic regression model, where explanatory variables are stochastic and not given and there exists no heteroskedasticity. The wild bootstrap procedure due to Davidson and Flachaire [The wild bootstrap, tamed at last, Working paper, IER#1000, Queen's University, 2001] with restricted residuals works best but its dominance is not strong compared to the result of Flachaire [Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap, Comput. Statist. Data Anal. 49 (2005), pp. 361–376] in the fixed regression model where explanatory variables are fixed and there exists heteroskedasticity.

Keywords:

• wild bootstrap
• pairs bootstrap
• stochastic explanatory variables
• uncorrelated but not independent explanatory variables and error term
• simulation

Mathematics Subject Classification :

• C12
• C15

Acknowledgements

The authors thank Emmanuel Flachaire for clarifying their questions and the referee for helpful comments. Hodoshima was financially supported for this work by Grant-in-Aid for Scientific Research (KAKENHI (19530184)). Ando was financially supported for this work by Grant-in-Aid for Scientific Research (KAKENHI (16.12163)).

Notes

We follow Flachaire 9 to call the test a t-test instead of a χ²-test, which might be considered a more appropriate name.