Generalized profiling estimation for global and adaptive penalized spline smoothing
Generalized profiling estimation for global and adaptive penalized spline smoothing
复制标题
DOI：
10.1016/j.csda.2008.12.004
复制
发表时间：
2009-05-15
影响因子：
1.8
通讯作者：
Ramsay, James O.
中科院分区：
文献类型：
--
作者：
Cao, Jiguo;Ramsay, James O.
We propose the generalized profiling method to estimate the multiple regression functions in the framework of penalized spline smoothing, where the regression functions and the smoothing parameter are estimated in two nested levels of optimization. The corresponding gradients and Hessian matrices are worked out analytically, using the Implicit Function Theorem if necessary, which leads to fast and stable computation. Our main contribution is developing the modified delta method to estimate the variances of the regression functions, which include the uncertainty of the smoothing parameter estimates. We further develop adaptive penalized spline smoothing to estimate spatially heterogeneous regression functions, where the smoothing parameter is a function that changes along with the curvature of regression functions. The simulations and application show that the generalized profiling method leads to good estimates for the regression functions and their variances. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.
