کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5129691 1489852 2017 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On some extensions of Bernstein's inequality for self-adjoint operators
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آمار و احتمال
پیش نمایش صفحه اول مقاله
On some extensions of Bernstein's inequality for self-adjoint operators
چکیده انگلیسی

We present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main feature of our bounds is that, unlike the majority of previous related results, they do not depend on the dimension d of the ambient space. Instead, the dimension factor is replaced by the “effective rank” associated with the underlying distribution that is bounded from above by d. In particular, this makes an extension to the infinite-dimensional setting possible. Our inequalities refine earlier results in this direction obtained by Hsu et al. (2012).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistics & Probability Letters - Volume 127, August 2017, Pages 111-119
نویسندگان
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