Minimax Hypothesis Testing.

Let X1,X2,...Xn be i.i.d. N-dimensional random variables having an unknown support of probability density denoted G; we suppose that G belongs to a functional class "g" of compact sets with smooth upper surface called boundary fragments. The problem consists in testing the hypotheses G=Go against alternative separated from the null hypotheses in uniform norm, respectively in Lebesgue measure of the symmetric difference by a value "&". Besides, we are interested in testing hypothesis on functionals of the density supports of the form integral in G. To solve these problems, we construct asymptotically minimax sequence of tests.