Fast Bivariate P-splines: the Sandwich Smoother

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	Fast Bivariate P-splines: the Sandwich Smoother
	Luo Xiao ; Yingxing Li ; David Ruppert
刊名	http://www.wise.xmu.edu.cn/paperInfor.asp?id=268
	2013-11-08
关键词	Asymptotics Bivariate smoothing Covariance function GLAM Nonparametric regression Penalized splines Sandwich smoother Thin plate splines.
英文摘要	We propose a fast penalized spline method for bivariate smoothing. Univariate Pspline smoothers Eilers and Marx (1996) are applied simultaneously along both coordinates. The new smoother has a sandwich form which suggested the name “sandwich smoother” to a referee. The sandwich smoother has a tensor product structure that simplifies an asymptotic analysis and it can be fast computed. We derive a local central limit theorem for the sandwich smoother, with simple expressions for the asymptotic bias and variance, by showing that the sandwich smoother is asymptotically equivalent to a bivariate kernel regression estimator with a product kernel. As far as we are aware, this is the first central limit theorem for a bivariate spline estimator of any type. Our simulation study shows that the sandwich smoother is orders of magnitude faster to compute than other bivariate spline smoothers, even when the latter are computed using a fast GLAM (Generalized Linear Array Model) algorithm, and comparable to them in terms of mean squared integrated errors. We extend the sandwich smoother to array data of higher dimensions, where a GLAM algorithm improves the computational speed of the sandwich smoother. One important application of the sandwich smoother is to estimate covariance functions in functional data analysis. In this application, our numerical results show that the sandwich smoother is orders of magnitude faster than local linear regression. The speed of the sandwich formula is important because functional data sets are becoming quite large.
语种	中文
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/56937]
专题	王亚南院－已发表论文
推荐引用方式 GB/T 7714	Luo Xiao,Yingxing Li,David Ruppert. Fast Bivariate P-splines: the Sandwich Smoother[J]. http://www.wise.xmu.edu.cn/paperInfor.asp?id=268,2013.
APA	Luo Xiao,Yingxing Li,&David Ruppert.(2013).Fast Bivariate P-splines: the Sandwich Smoother.http://www.wise.xmu.edu.cn/paperInfor.asp?id=268.
MLA	Luo Xiao,et al."Fast Bivariate P-splines: the Sandwich Smoother".http://www.wise.xmu.edu.cn/paperInfor.asp?id=268 (2013).