Tests of non-nested regression models some results on small sample behaviour and the bootstrap

The most popular procedures for testing a regression model against a single non-nested alternative can be substantially oversized in small samples. Also, when a regression model is to be tested in the presence of several non-nested alternatives, the null model is sometimes accepted only if testing against each alternative in turn produces no significant outcomes. This approach leads to an implicit overall test with a significance level that is not known, even asymptotically. It is shown that the bootstrap can be used to control significance levels in both types of situation. Power estimates for various tests using bootstrap critical values are also obtained and compared.