Browsing by Author "Huang, Hsin-Cheng"

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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.
On selection of spatial linear models for lattice data
(2010)
Zhu, Jun
;
Huang, Hsin-Cheng
;
Reyes, Perla E.
;
交大名義發表
;
National Chiao Tung University
Spatial linear models are popular for the analysis of data on a spatial lattice, but statistical techniques for selection of covariates and a neighbourhood structure are limited. Here we develop new methodology for simultaneous model selection and parameter estimation via penalized maximum likelihood under a spatial adaptive lasso. A computationally efficient algorithm is devised for obtaining approximate penalized maximum likelihood estimates. Asymptotic properties of penalized maximum likelihood estimates and their approximations are established. A simulation study shows that the method proposed has sound finite sample properties and, for illustration, we analyse an ecological data set in western Canada.
Regularized Principal Component Analysis for Spatial Data
(2017-01-01)
Wang, Wen-Ting
;
Huang, Hsin-Cheng
;
統計學研究所
;
Institute of Statistics
In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations and n time points with the possibility that p > n. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when p is large relative to n. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical examples.
Regularized spatial maximum covariance analysis
(2018-03-01)
Wang, Wen-Ting
;
Huang, Hsin-Cheng
;
統計學研究所
;
Institute of Statistics
In climate and atmospheric research, many phenomena involve more than one spatial processes covarying in space. To understand how one process is affected by another, maximum covariance analysis is commonly applied. However, the patterns obtained from maximum covariance analysis may sometimes be difficult to interpret. In this paper, we propose a regularization approach to promote spatial features in dominant coupled patterns by introducing smoothness and sparseness penalties while accounting for their orthogonalities. We develop an efficient algorithm to solve the resulting optimization problem by using the alternating direction method of multipliers. The effectiveness of the proposed method is illustrated by several numerical examples, including an application to study how precipitation in East Africa is affected by sea surface temperatures in the Indian Ocean.