As a competitive depth, L^2-depth is modified from L^2-depth. Its induced median is called L^2-median. Basic properties of the median and its sample version are provided. Especially, the strong consistency of sample m...As a competitive depth, L^2-depth is modified from L^2-depth. Its induced median is called L^2-median. Basic properties of the median and its sample version are provided. Especially, the strong consistency of sample median is gained under weaker condition. Robustness of the median and its sample version is discussed. Besides ease of computation, it is shown that L^2-median has both good large-sample and robust properties. Simulation studies are also given to compare the breakdown point of L^2-median with that of other depth-induced medians.展开更多
基金This research is supported by the National Natural Science Foundation of China under Grant No. 10971007, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20091103120012, and the research fund of B JUT under Grant No. X0006013200904. The authors greatly appreciate the constructive comments by the three anonymous reviewers and an associate editor. This has led to substantial improvements in our paper. Special thanks to financial support from the Science and Technology Development Fund of the Government of the Macao Special Administrative Region （No. 045/2005/A）.
文摘As a competitive depth, L^2-depth is modified from L^2-depth. Its induced median is called L^2-median. Basic properties of the median and its sample version are provided. Especially, the strong consistency of sample median is gained under weaker condition. Robustness of the median and its sample version is discussed. Besides ease of computation, it is shown that L^2-median has both good large-sample and robust properties. Simulation studies are also given to compare the breakdown point of L^2-median with that of other depth-induced medians.
