EQUIVALENCE OF NETWORK STRUCTURES IN NETWORKS OF RANDOM VARIABLES WITH KNOWN AND UNKNOWN SHIFT PARAMETER

摘要

It is proved that a sign network with an elliptical distribution with known shift parameter is equivalent to a sign network with elliptical distribution with unknown shift parameter estimated by sample mean. This result is proved for the case of independent identically distributed observations and for the case of sample from a matrix elliptically contoured distribution with any dependence between observations.