Non-parametric Regression Tests Using Dimension Reduction Techniques

Testing for parametric structure is an important issue in non-parametric regression analysis. A standard approach is to measure the distance between a parametric and a non-parametric fit with a squared deviation measure. These tests inherit the curse of dimensionality from the non-parametric estimator. This results in a loss of power in finite samples and against local alternatives. This article proposes to circumvent the curse of dimensionality by projecting the residuals under the null hypothesis onto the space of additive functions. To estimate this projection, the smooth backfitting estimator is used. The asymptotic behaviour of the test statistic is derived and the consistency of a wild bootstrap procedure is established. The finite sample properties are investigated in a simulation study. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008.