Statistical Testability of Uncertainty Models

Statistical model validation is treated for a general class of nonparamet-ric uncertainty models. This problem is shown to reduce, in many cases of interest, to computing the limit of a sequence (V k) 1 1 of relative weighted volumes of convex sets in R k. An associated decision problem is shown to reduce to a pair of likelihood ratio tests. The notion of testability is introduced to describe uncertainty models that can be statistically validated with arbitrary reliability using input-output data records of suucient ((nite) length. It is then shown that some common uncertainty models, such as those involving`1 or H 1 norms, do not possess this property.