Test for Linearity in Non-Parametric Regression Models

Abstract

The problem of checking the linearity of a regression relationship is addressed. The test uses nonparametric estimation techniques. The null hypothesis is that the regression function is linear; it is tested against the non-specic alternatives hypotheses. This test is based on a Hermite transform characterization of conditional expectations. A statistical test is derived, the distribution of this statistic under the null hypothesis of linearity is determined. A power study using simulation shows the new statistic to be more sensitive to non-linearity.