Resampling-type error rate estimation for linear discriminant functions: Pearson VII distributions

Abstract This paper extends the work of a previous paper on error rate estimation for linear descriminant functions by considering additional non-Gaussian distributions from the Pearson VII family. The Pearson VII family is an elliptically contoured family of probability densities with a parameter m that controls the tail length of the distribution. For m > 2 (i.e. reasonably light tails) the estimators perform similarly to previous Gaussian case studies and previous simulated exponential and uniform distributions. For m ⩽ 1.6 (i.e. heavy tails) results similar to previous Cauchy cases are obtained. The 0.632 estimator generally performed best for large m, but it does not perform as well as the e0 and convex bootstrap when the tails are heavy. The positive bias of e0 no longer pertains when the tails are heavy.