Penalized regression with model‐based penalties

作者：Nancy Heckman, J. O. Ramsay · 发表于：Canadian Journal of Statistics · 年份：2000 · DOI：10.2307/3315976 · 被引用次数：123 · 研究领域：Statistical Methods and Inference、Control Systems and Identification、Probabilistic and Robust Engineering Design

Abstract Nonparametric regression techniques such as spline smoothing and local fitting depend implicitly on a parametric model. For instance, the cubic smoothing spline estimate of a regression function ∫ μ based on observationsti,Yi is the minimizer of Σ{Yi ‐ μ(ti)}2+ λ∫(μ′′)2. Since ∫(μ″)2is zero when μ is a line, the cubic smoothing spline estimate favors the parametric model μ(t) = αo+ α1t. Here the authors consider replacing ∫(μ″)2with the more general expression ∫(Lμ)2whereLis a linear differential operator with possibly nonconstant coefficients. The resulting estimate of μ performs well, particularly ifLμ is small. They present an O(n) algorithm for the computation of μ. This algorithm is applicable to a wide class ofL's. They also suggest a method for the estimation ofL. They study their estimates via simulation and apply them to several data sets.