  The thin plate spline smoother is a classical model for fnding a smooth
function from the knowledge of its observation at scattered locations which may
have random noises. We consider a nonconforming Morley finite element method to
approximate the model. We prove the stochastic convergence of the finite
element method which characterizes the tail property of the probability
distribution function of the finite element error. We also propose a
self-consistent iterative algorithm to determine the smoothing parameter based
on our theoretical analysis. Numerical examples are included to confirm the
theoretical analysis and to show the competitive performance of the self-
consistent algorithm for finding the smoothing parameter.
