There have two random variables, each of which is of five dimension. One random variable tracks the data collected from one device. The other random variable represents the data collected from another device. I would like to see whether these two devices are replaceable with each other by measuring the similarity of these two random variables.
Naturally, there have some distance metrics to quantify the difference. However, these distances only tell us the comparative differences used for clustering or classification. The problem here is that we only have two random variables here, and need a kind of “absolute distance” to quantify the similarity.
Another challenge is that if we cannot find the underlying probability distribution for these two random variables, are there any non-parametric methods for this?