The concern here is retrieval of harmonic observed in multiplicative and complex additive noises. Cyclic mean and correlation statistics have proved to be useful for harmonic retrieval in the presence of real-valued multiplicative and complex-valued additive noise of arbitrary color and distribution. Performance analysis of cyclic estimators is carried through both for nonzero and zero mean multiplicative noises. Cyclic estimators are shown to be asymptotically equivalent to certain nonlinear least squares estimators, and large sample variance expressions of the cyclic estimators are derived. Simulations validate the large sample performance analysis.