  We consider the problems of confidence estimation and hypothesis testing on a
parameter of signal observed in Gaussian white noise. For these problems we
point out lower bounds of asymptotic efficiency in the zone of moderate
deviation probabilities. These lower bounds are versions of local asymptotic
minimax Hajek-Le Cam lower bound in estimation and the lower bound for Pitman
efficiency in hypothesis testing. The lower bounds were obtained for both
logarithmic and sharp asymptotic of moderate deviation probabilities.
