Kernel density estimation on the rotation group and its application to crystallographic texture analysis
نویسندگان
چکیده
منابع مشابه
Kernel density estimation on the rotation group and its application to crystallographic texture analysis
We are concerned with kernel density estimation on the rotation group SO(3). We prove asymptotically optimal convergence rates for the minimax risk of the mean integrated squared error for different function classes including bandlimited functions, functions with bounded Sobolev norm and functions with polynomial decaying Fourier coefficients and give optimal kernel functions. Furthermore, we c...
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In many applications, the collected data takes values in a manifold rather than in an Euclidian space. Numerous examples of such datasets can be found in the fields of robotics, satellite control attitude, chemistry, crystallography [1]. In statistics, many applications have lead to the study of datasets on spheres or oriented frames [2] as well as on special matrix manifolds (Grassmann and Sti...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 2013
ISSN: 0047-259X
DOI: 10.1016/j.jmva.2013.03.014