کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5129588 | 1489739 | 2017 | 17 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Penalized B-spline estimator for regression functions using total variation penalty Penalized B-spline estimator for regression functions using total variation penalty](/preview/png/5129588.png)
We carry out a study on a penalized regression spline estimator with total variation penalty. In order to provide a spatially adaptive method, we consider total variation penalty for the estimating regression function. This paper adopts B-splines for both numerical implementation and asymptotic analysis because they have small supports, so the information matrices are sparse and banded. Once we express the estimator with a linear combination of B-splines, the coefficients are estimated by minimizing a penalized residual sum of squares. A new coordinate descent algorithm is introduced to handle total variation penalty determined by the B-spline coefficients. For large-sample inference, a nonasymptotic oracle inequality for penalized B-spline estimators is obtained. The oracle inequality is then used to show that the estimator is an optimal adaptive for the estimation of the regression function up to a logarithm factor.
Journal: Journal of Statistical Planning and Inference - Volume 184, May 2017, Pages 77-93