A Wiener system, i.e., a system comprising a linear dynamic and a nonl
inear memoryless subsystems connected in a cascade, is identified. Bot
h the input signal and disturbance are random, white, and Gaussian. Th
e unknown nonlinear characteristic is strictly monotonous and differen
tiable and, therefore, the problem of its recovering from input-output
observations of the whole system is nonparametric. It is shown that t
he inverse of the characteristic is a regression function and, next, a
class of orthogonal series nonparametric estimates recovering the reg
ression is proposed and analyzed. The estimates apply the trigonometri
c, Legendre, and Hermite orthogonal functions. Pointwise consistency o
f all the algorithms is shown. Under some additional smoothness restri
ctions, the rates of their convergence are examined and compared. An a
lgorithm to identify the impulse response of the linear subsystem is p
roposed.