A link-free method for testing the significance of predictors

One important step in regression analysis is to identify significant predictors from a pool of candidates so that a parsimonious model can be obtained using these significant predictors only. However, most of the existing methods assume linear relationships between response and predictors, which may be inappropriate in some applications. In this article, we discuss a link-free method that avoids specifying how the response depends on the predictors. Therefore, this method has no problem of model misspecification, and it is suitable for selecting significant predictors at the preliminary stage of data analysis. A test statistic is suggested and its asymptotic distribution is derived. Examples are used to demonstrate the proposed method.