Browsing by Author "Chen, Chun-Shu"

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An improved C(p) criterion for spline smoothing
(2011-01-01)
Chen, Chun-Shu
;
Huang, Hsin-Cheng
;
統計學研究所
;
Institute of Statistics
Spline smoothing is a popular technique for curve fitting, in which selection of the smoothing parameter is crucial. Many methods such as Mallows' C(p), generalized maximum likelihood (GML), and the extended exponential (EE) criterion have been proposed to select this parameter. Although C(p) is shown to be asymptotically optimal, it is usually outperformed by other selection criteria for small to moderate sample sizes due to its high variability. On the other hand, GML and EE are more stable than C(p), but they do not possess the same asymptotic optimality as C(p). Instead of selecting this smoothing parameter directly using C(p), we propose to select among a small class of selection criteria based on Stein's unbiased risk estimate (SURE). Due to the selection effect, the spline estimate obtained from a criterion in this class is nonlinear. Thus, the effective degrees of freedom in SURE contains an adjustment term in addition to the trace of the smoothing matrix, which cannot be ignored in small to moderate sample sizes. The resulting criterion, which we call adaptive C(p), is shown to have an analytic expression, and hence can be efficiently computed. Moreover, adaptive C(p) is not only demonstrated to be superior and more stable than commonly used selection criteria in a simulation study, but also shown to possess the same asymptotic optimality as C(p). (C) 2010 Elsevier B.V. All rights reserved.
An improved C-p criterion for spline smoothing
(2011-01-01)
Chen, Chun-Shu
;
Huang, Hsin-Cheng
;
統計學研究所
;
Institute of Statistics
Spline smoothing is a popular technique for curve fitting, in which selection of the smoothing parameter is crucial. Many methods such as Mallows' C-p, generalized maximum likelihood (GML), and the extended exponential (EE) criterion have been proposed to select this parameter. Although C-p is shown to be asymptotically optimal, it is usually outperformed by other selection criteria for small to moderate sample sizes due to its high variability. On the other hand, GML and EE are more stable than C-p, but they do not possess the same asymptotic optimality as C-p. Instead of selecting this smoothing parameter directly using C-p, we propose to select among a small class of selection criteria based on Stein's unbiased risk estimate (SURE). Due to the selection effect, the spline estimate obtained from a criterion in this class is nonlinear. Thus, the effective degrees of freedom in SURE contains an adjustment term in addition to the trace of the smoothing matrix, which cannot be ignored in small to moderate sample sizes. The resulting criterion, which we call adaptive C-p, is shown to have an analytic expression, and hence can be efficiently computed. Moreover, adaptive C-p is not only demonstrated to be superior and more stable than commonly used selection criteria in a simulation study, but also shown to possess the same asymptotic optimality as C-p. (C) 2010 Elsevier B.V. All rights reserved.
Geostatistical model averaging based on conditional information criteria
(2012-03-01)
Chen, Chun-Shu
;
Huang, Hsin-Cheng
;
統計學研究所
;
Institute of Statistics
Variable selection in geostatistical regression is an important problem, but has not been well studied in the literature. In this paper, we focus on spatial prediction and consider a class of conditional information criteria indexed by a penalty parameter. Instead of applying a fixed criterion, which leads to an unstable predictor in the sense that it is discontinuous with respect to the response variables due to that a small change in the response may cause a different model to be selected, we further stabilize the predictor by local model averaging, resulting in a predictor that is not only continuous but also differentiable even after plugging-in estimated model parameters. Then Stein's unbiased risk estimate is applied to select the penalty parameter, leading to a data-dependent penalty that is adaptive to the underlying model. Some numerical experiments show superiority of the proposed model averaging method over some commonly used variable selection methods. In addition, the proposed method is applied to a mercury data set for lakes in Maine.