On the estimates of the signal, its derivatives and the point of maximum for Gaussian observations

We propose the estimates of the «signal» $S(t)$ and of its derivatives for the case when the observed process $X_\varepsilon(t)$ has the form (0.1). These estimates have asymptotically optimal rate of convergence to the unknown value of the «parameter» for a wide class of a priori assumptions on $S$ and on the loss functions. The analogous results for the estimates of the point of maximum of $S(t)$ are obtained also.