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Nonconcave Penalized Spline

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.