https://scholars.lib.ntu.edu.tw/handle/123456789/30223
標題: | Methods For Tracking Support Boundaries with Corners | 作者: | Cheng, Ming-Yen Hall, Peter |
關鍵字: | Bandwidth;boundary;corner;curvature;frontier;kernel method;local linear;nonparametric curve estimation;support | 公開日期: | 2006 | 起(迄)頁: | 1870-1893 | 來源出版物: | Journal of Multivariate Analysis 97 | 摘要: | In a range of practical problems the boundary of the support of a bivariate distribution is of interest, for example where it describes a limit to e±- ciency or performance, or where it determines the physical extremities of a spatially distributed population in forestry, marine science, medicine, meteorology or geol- ogy. We suggest a tracking-based method for estimating a support boundary when it is composed of a ¯nite number of smooth curves, meeting together at corners. The smooth parts of the boundary are assumed to have continuously turning tan- gents & bounded curvature, & the corners are not allowed to be in¯nitely sharp; that is, the angle between the two tangents should not equal ¼. In other respects, however, the boundary may be quite general. In particular it need not be uniquely de¯ned in Cartesian coordinates, its corners my be either concave or convex, and its smooth parts may be neither concave nor convex. Tracking methods are well suited to such generalities, & they also have the advantage of requiring relatively small amounts of computation. It is shown that they achieve optimal convergence rates, in the sense of uniform approximation. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/20060927121126023390 | 其他識別: | 20060927121126023390 |
顯示於: | 數學系 |
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ch-track2.pdf | 284.5 kB | Adobe PDF | 檢視/開啟 |
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