数学
平滑样条曲线
估计员
点式的
花键(机械)
平滑的
分段
单变量
非参数回归
薄板样条
应用数学
数学优化
统计
样条插值
数学分析
双线性插值
多元统计
结构工程
工程类
作者
David Ruppert,Raymond J. Carroll
标识
DOI:10.1111/1467-842x.00119
摘要
The paper studies spline fitting with a roughness penalty that adapts to spatial heterogeneity in the regression function. The estimates are p th degree piecewise polynomials with p − 1 continuous derivatives. A large and fixed number of knots is used and smoothing is achieved by putting a quadratic penalty on the jumps of the p th derivative at the knots. To be spatially adaptive, the logarithm of the penalty is itself a linear spline but with relatively few knots and with values at the knots chosen to minimize the generalized cross validation (GCV) criterion. This locally‐adaptive spline estimator is compared with other spline estimators in the literature such as cubic smoothing splines and knot‐selection techniques for least squares regression. Our estimator can be interpreted as an empirical Bayes estimate for a prior allowing spatial heterogeneity. In cases of spatially heterogeneous regression functions, empirical Bayes confidence intervals using this prior achieve better pointwise coverage probabilities than confidence intervals based on a global‐penalty parameter. The method is developed first for univariate models and then extended to additive models.
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