Splines, Knots, and Penalties
نویسندگان
چکیده
Penalized splines have gained much popularity as a flexible tool for smoothing and semi-parametric models. Two approaches have been advocated: 1) use a B-spline basis, equally-spaced knots and difference penalties (Eilers and Marx, 1996) and 2) use truncated power functions, knots based on quantiles of the independent variable and a ridge penalty (Ruppert, Wand and Carroll, 2003). We compare the two approaches on many aspects: numerical stability, quality of the fit, interpolation/extrapolation, derivative estimation, visual presentation and extension to multi-dimensional smoothing. We discuss mixed model and Bayesian parallels to penalized regression. We conclude that B-splines with difference penalties are clearly to be preferred.
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