کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1147707 957787 2011 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Kernel density estimation on the torus
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Kernel density estimation on the torus
چکیده انگلیسی

Kernel density estimation for multivariate, circular data has been formulated only when the sample space is the sphere, but theory for the torus would also be useful. For data lying on a d  -dimensional torus (d⩾1)(d⩾1), we discuss kernel estimation of a density, its mixed partial derivatives, and their squared functionals. We introduce a specific class of product kernels whose order is suitably defined in such a way to obtain L2-risk formulas whose structure can be compared to their Euclidean counterparts. Our kernels are based on circular densities; however, we also discuss smaller bias estimation involving negative kernels which are functions of circular densities. Practical rules for selecting the smoothing degree, based on cross-validation, bootstrap and plug-in ideas are derived. Moreover, we provide specific results on the use of kernels based on the von Mises density. Finally, real-data examples and simulation studies illustrate the findings.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 141, Issue 6, June 2011, Pages 2156–2173
نویسندگان
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