  In this paper, we study the Tikhonov regularization scheme in Hilbert scales
for the nonlinear statistical inverse problem with a general noise. The
regularizing norm in this scheme is stronger than the norm in Hilbert space. We
focus on developing a theoretical analysis for this scheme based on the
conditional stability estimates. We utilize the concept of the distance
function to establish the high probability estimates of the direct and
reconstruction error in Reproducing kernel Hilbert space setting. Further, the
explicit rates of convergence in terms of sample size are established for the
oversmoothing case and the regular case over the regularity class defined
through appropriate source condition. Our results improve and generalize
previous results obtained in related settings.
