High Dimensional Statistics学习笔记(一):Sub-Gaussian Random Variables 陆加柒等于十三 UCAS|Statistics 19 人赞同了该文章 该笔记主要参考:ocw.mit.edu/courses/18-SUB-GAUSSIAN RANDOM VARIABLES AND CHERNOFF BOUNDS 引入sub-Gaussian分布的动机,主要是考虑Gaussian分布的强尾衰减:若...
Buldygin, V. V. and Kozachenko, Y. V. (1980). “Sub-Gaussian random variables.” Ukrainian Mathematical Journal , Vol. 32, No. 6, pp. 483–489. MathSciNetBuldygin, V.V. and Kozacˇenko, J.V. (1980). Sub-Gaussian random variables. Ukrain. Mat. Zh. 32 723-730. MR0598605VV...
, which form a very interest subclass of Subgaussian (Sub) r.v., and obtain the exact exponential bounds for tail of distribution for sums of independent and disjoint such a variables, not necessary to be identical distributed, and give some new examples of SSub variables to show the ...
The almost sure convergence of weighted sums of φ-subgaussian m-acceptable random variables is investigated. As corollaries, the main results are applied to the case of negatively dependent and m-dependent subgaussian random variables. Finally, an application to random Fourier series is presented....
In this paper, we provide a proof for the Hanson-Wright inequalities for sparsified quadratic forms in subgaussian random variables. This provides useful concentration inequalities for sparse subgaussian random vectors in two ways. Let X = (X_1, \\ldots, X_m) \\in \\mathbb{R}^m X = ...
A crucial problem for on-line independent component analysis (ICA) algorithm is the choice of step-size, which reflects a tradeoff between steady-state error and convergence speed. This paper proposes a novel ICA algorithm for sub-Gaussian sources, which converges fast while maintaining low steady...
Moreprecisely, let {X_n,n=1,2,...} be a sequence of φ-subgauss-ian random variables and {D_n,n=1,2,...} be an arbitrary sequence of random variables. We consider the convergence of the series a_1*X_1*cos(t+D_1)+...+a_n*X_n*cos(nt+D_n)+...,0≦t≦2π to a...
Hoeffding inequalityBoundedSub-GaussianWhen addressing various financial problems,such as estimating stock portfolio risk,it is necessary to derive the distribution of the sum of the dependent random variables.Although deriving this distribution requires identifying the joint distribution of these random ...
VOLODIN, Convergence of series of dependent ϕ -sub- Gaussian random variables, J. Math. Anal. Appl. 338, no. 2 (2008), 1188-1203.R. G. Antonioni, Y. Kozachenko, A. Volodin, "Convergence of series of de- pendent φ-subgaussian random variables," Journal of Mathematical Analysis and...
We show bounds on tail probabilities for quadratic forms in sub-gaussian not necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned bounds. As an example we give estimates of tail ...