A simulation study of the finite-sample performance of the sample scale curve as an estimator of its population counterpart

Abstract

The depth-based scale curves have broad applications in nonparametric multivariate statistics. Many nonparametric multivariate measures and procedures are based on the scale curves. In this article, we study the finite-sample performance of the sample scale curve as an estimator of its population counterpart by simulation. It is found that the sample scale curve tends to underestimate its population counterpart and that the discrepancy increases quickly as dimension increases. The effect of data shape characterized by kurtosis on the performance is also studied. Compared with the effect of dimension, the effect of kurtosis is minor. The root cause of the issue is explored and some suggestions for improvement are provided.

Keywords:

• Simulation
• Convex hull
• Depth function
• Ellipsoid hull
• Nonparametric multivariate method
• Scale curve

AMS 2000 SUBJECT CLASSIFICATION:

• Primary 62G05 Secondary 62H05

Acknowledgments

Many thanks are due to an anonymous referee and the Editor-in-Chief, Prof. Narayanaswamy Balakrishnan, for their insightful comments and valuable suggestions, which led to considerable improvements in this article. Also, support by the Perko Faculty Research Award of Northern Arizona University is gratefully acknowledged.

Disclosure statement

None.