Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on $\mathbb{ E} = [0, \infty]^d \backslash \{ (0,0, ..., 0) \} $ and models another regular variation on the sub-cone $\mathbb{ E}^{ (2)} = \mathbb{ E} \backslash \cup_{ i=1}^d \mathbb{ L}_i$, where $\mathbb{ L}_i$ is the $i$-th axis. We extend the concept of hidden regular variation to sub-cones of $\mathbb{ E}^{ (2)}$ as well. We suggest a procedure for detecting the presence of hidden regular variation, and if it exists, propose a method of estimating the limit measure exploiting its semi-parametric structure. We exhibit examples where hidden regular variation yields better estimates of probabilities of risk sets.
Categories: math.PR math.ST q-fin.RM stat.TH
