On the Use of Nonparametric Regression for Checking Linear Relationships

Abstract

SUMMARY The problem of checking the linearity of a regression relationship is addressed through the idea of smoothing of a residual plot. A pseudolikelihood ratio test statistic, which measures the distance between the nonparametric and the parametric models, is derived as a ratio of quadratic forms. The distribution of this statistic under the null hypothesis of linearity is calculated numerically by using Johnson curves. A power study shows the new statistic to be more sensitive to non-linearity than the Durbin-Watson statistic.