The trade-off between robustness and efficiency and the effect of model smoothing in minimum disparity inference

Abstract

Through an empirical study at the normal model it is shown that the curvature parameter of the residual adjustment function (Lindsay 1994) is not always an adequate global measure of the trade-off between robustness and efficiency of the minimum disparity estimators. Our study shows that the estimator obtained by minimizing the negative exponential disparity is an attractive robust estimator with good efficiency properties. Smoothing the model with the same kernel used to determine the nonparametric density estimator results in higher efficiency for the minimum disparity estimators, especially for the estimator of the scale parameter. In addition the disparity tests (including the negative exponential disparity test) are shown to be good robust alternatives to the likelihood ratio test at the normal model.

Keywords:

• Hellinger distance
• Negative exponential disparity
• Disparity tests
• Estimation cur-vature
• Residual adjustment function
• Kernel density estimator