Nonparametric estimation of a change point in positive shift models

Abstract

Six nonparametric estimators of the change point are compared via Monte Carlo simulation in positive shift models of widely different taillengths. It is found that the best estimator in terms of smallest mean-squared error depends on the taillength of the underlying distribution. Overall, an estimator of Lombard (1987) based on a Wilcoxon scores rank statistic is recommended.

Keywords:

• change point
• generalized lambda family
• mean-squared error
• shift model