Testing linearity in semiparametric regression models

One of the fundamental assumptions of a basic multiple linear regression model is that the contribution of each of the model terms is strictly linear. In many cases, this may be an excessive simplification of the complicated relationships. Moreover, it may be difficult or impossible to test the hypothesized model against all possible kinds of relevant alternative models. Therefore, tests that perform well under more general circumstances are also required. This paper considers the semiparametric model, where the contribution of one of the model terms may not be strictly linear, and also proposes an exact F-test for the situation. The method also allows dependent error terms. The performance of the proposed test is illustrated by simulation experiments and in real air pollution and health data.