  Regression spline is a useful tool in nonparametric regression. However,
finding the optimal knot locations is a known difficult problem. In this
article, we introduce the Non-concave Penalized Regression Spline. This
proposal method not only produces smoothing spline with optimal convergence
rate, but also can adaptively select optimal knots simultaneously. It is
insensitive to the number of origin knots. The method's performance in a
simulation has been studied to compare the other methods. The problem of how to
choose smoothing parameters, i.e. penalty parameters in the non-concave
regression spline is addressed.
