Asymptotically efficient signal estimation in L₂ under the general loss functions

The problem of nonparametric signal estimation in the gaussian white noise is studied. Asymptotics of the minimax L₂-risk on ellipsoids in non-square loss functions is obtained. The degenerated character of the minimax risk asymptotics is explicitly described. A random process satisfying the stochastic differential equation with the standard Wigner process is considered.