Estimating functions and derivatives via adaptive penalized splines.

Adaptive penalized splines via radial basis are constructed to estimate regression functions and their derivatives. A weight vector based on the range of observations is embedded into the penalty matrix, which remarkably improves the adaptability of the penalized spline smoothing model. Fast computation and comparison with traditional spline models are studied, and the empirical results and simulations show that the new method outperforms smoothing splines, traditional penalized splines and local polynomial smoothing when estimating regression functions and their derivatives, particularly when the observations have inhomogeneous variation. [ABSTRACT FROM AUTHOR]