淡江大學機構典藏:Item 987654321/55592
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    Title: Estimation of 2D jump location curve and 3D jump location surface in nonparametric regression
    Authors: Chu, Chih-Kang;Siao, Jhao-Siang;Wang, Lih-Chung;Deng, Wen-Shuenn
    Contributors: 淡江大學統計學系
    Keywords: Jump location curve;Jump location surface;Kernel smoothing method;Nonparametric jump regression model;Rotational difference kernel estimate;Ridge location
    Date: 2012-01
    Issue Date: 2011-08-23 23:39:06 (UTC+8)
    Publisher: New York: Springer New York LLC
    Abstract: A new procedure is proposed to estimate the jump location curve and surface in the two-dimensional (2D) and three-dimensional (3D) nonparametric jump regression models, respectively. In each of the 2D and 3D cases, our estimation procedure is motivated by the fact that, under some regularity conditions, the ridge location of the rotational difference kernel estimate (RDKE; Qiu in Sankhyā Ser. A 59, 268–294, 1997, and J. Comput. Graph. Stat. 11, 799–822, 2002; Garlipp and Müller in Sankhyā Ser. A 69, 55–86, 2007) obtained from the noisy image is asymptotically close to the jump location of the true image. Accordingly, a computational procedure based on the kernel smoothing method is designed to find the ridge location of RDKE, and the result is taken as the jump location estimate. The sequence relationship among the points comprising our jump location estimate is obtained. Our jump location estimate is produced without the knowledge of the range or shape of jump region. Simulation results demonstrate that the proposed estimation procedure can detect the jump location very well, and thus it is a useful alternative for estimating the jump location in each of the 2D and 3D cases.
    Relation: Statistics and Computing 22(1), pp.17-31
    DOI: 10.1007/s11222-010-9203-2
    Appears in Collections:[Graduate Institute & Department of Statistics] Journal Article

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