On the consistency of a spatial-type interval-valued median for random intervals

The sample $d_{\theta }$-median is a robust estimator of the central tendency or location of an interval-valued random variable. While the interval-valued sample mean can be highly influenced by outliers, this spatial-type interval-valued median remains much more reliable. In this paper, we show that under general conditions the sample $d_{\theta }$-median is a strongly consistent estimator of the $d_{\theta }$-median of an interval-valued random variable.