Bootstrap hypothesis testing in regression models

The paper investigates how the particular choice of residuals used in a bootstrap-based testing procedure affects the properties of the test. The properties of the tests are investigated both under the null and under the alternative. It is shown that for non-pivotal test statistics, the method used to obtain residuals largely affects the power behavior of the tests. For instance, imposing the null hypothesis in the residual estimation step--although it does not affect the behavior of the test if the null is true--it leads to a loss of power under the alternative as compared to tests based on resampling unrestricted residuals. Residuals obtained using a parameter estimator which minimizes their variance maximizes the power of the corresponding bootstrap-based tests. In this context, studentizing makes the tests more robust to such residual effects.