  This paper focuses on self-similar gravitational collapse solutions of the
Einstein--axion-dilaton configuration for two conjugacy classes of SL(2, R)
transformations. These solutions are invariant under spacetime dilation,
combined with internal transformations. For the first time in
Einstein--axion-dilaton literature, we apply the nonlinear statistical spline
regression methods to estimate the critical spherical black hole solutions in
four dimension. These spline methods include truncated power basis, natural
cubic spline and penalized B-spline. The prediction errors of the statistical
models, on average, are almost less than $10^{-2}$, so all the developed models
can be considered unbiased estimators for the critical collapse functions over
their entire domains. In addition to this excellence, we derived closed forms
and continuously differentiable estimators for all the critical collapse
functions.
