中位数的Jensen不等式

The Superiority of a Kind of Empirical Bayes Estimator

在一定条件下,用中位数来替代Jensen不等式中的期望,不等式同样地成立.本文给出了关于中位数的一个新的定义,从而可以把该不等式自然地推广到高维的情形.

Under some conditions, we prove an analogue of Jensen inequality, with medians instead of means. A novel definition of a median is given, which allows a natural extension to higher dimensions.