کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
11005592 | 1489632 | 2018 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Simplicial variances, potentials and Mahalanobis distances
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز عددی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The average squared volume of simplices formed by k independent copies from the same probability measure μ on Rd defines an integral measure of dispersion Ïk(μ), which is a concave functional of μ after suitable normalization. When k=1 it corresponds to tr(Σμ)
and when k=d we obtain the usual generalized variance det(Σμ), with Σμ the covariance matrix of μ. The dispersion Ïk(μ) generates a notion of simplicial potential at any xâRd, dependent on μ. We show that this simplicial potential is a quadratic convex function of x, with minimum value at the mean aμ for μ, and that the potential at aμ defines a central measure of scatter similar to Ïk(μ), thereby generalizing results by Wilks (1960) and van der Vaart (1965) for the generalized variance. Simplicial potentials define generalized Mahalanobis distances, expressed as weighted sums of such distances in every k-margin, and we show that the matrix involved in the generalized distance is a particular generalized inverse of Σμ, constructed from its characteristic polynomial, when k=rank(Σμ). Finally, we show how simplicial potentials can be used to define simplicial distances between two distributions, depending on their means and covariances, with interesting features when the distributions are close to singularity.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 168, November 2018, Pages 276-289
Journal: Journal of Multivariate Analysis - Volume 168, November 2018, Pages 276-289
نویسندگان
Luc Pronzato, Henry P. Wynn, Anatoly A. Zhigljavsky,