In this book, we propose a function estimation procedure using adaptive free-knot splines (AFKS) and associated algorithm for implementation in nonparametric regression. Knot selection is extremely important for estimating a function with complicated structure by spline functions. The AFKS allows variable knot numbers and replacements of knots at any locations and multiple knots at the same location. This flexibility leads to an adaptive spline estimator that adapts to any function with inhomogeneous smoothness, including a sharp kink or discontinuity, which substantially improves the...