Journal ArticleDOI
Independent and stationary sequences of random variables
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This article is published in Bulletin of The London Mathematical Society.The article was published on 1973-11-01. It has received 376 citations till now. The article focuses on the topics: Random variable.read more
Citations
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The Jackknife and the Bootstrap for General Stationary Observations
TL;DR: In this article, the authors extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence, and they show that consistency is obtained if $l = l(n) \rightarrow \infty$ and $l(n)/n \ rightarrow 0$.
Book
Chance and Stability: Stable Distributions and Their Applications
TL;DR: In this article, the authors introduce the theory of stable laws and apply it to some probabilistic models correlated systems and fractals anomalous diffusion and chaos physics radiophysics astrophysics and cosmology.
Journal ArticleDOI
Large Deviations of Sums of Independent Random Variables
TL;DR: In this article, various variants of bounds for probabilities of large deviations of sums of independent random variables in terms of ordinary and generalized moments of individual summands are discussed. And a great deal of attention is devoted to the study of the precision of these bounds.
Book
Eigenvalue Distribution of Large Random Matrices
Leonid Pastur,Mariya Shcherbina +1 more
TL;DR: Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and related sciences as mentioned in this paper, which is a good reference for researchers in various areas of mathematics and mathematical physics.
Journal ArticleDOI
Fixed-width output analysis for Markov chain Monte Carlo
TL;DR: In this article, the authors consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user-specified value.
References
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Journal ArticleDOI
The Jackknife and the Bootstrap for General Stationary Observations
TL;DR: In this article, the authors extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence, and they show that consistency is obtained if $l = l(n) \rightarrow \infty$ and $l(n)/n \ rightarrow 0$.
BookDOI
Combinatorial Stochastic Processes
TL;DR: In this paper, the Brownian forest and the additive coalescent were constructed for random walks and random forests, respectively, and the Bessel process was used for random mappings.
Journal ArticleDOI
Regularized estimation of large covariance matrices
Peter J. Bickel,Elizaveta Levina +1 more
TL;DR: If the population covariance is embeddable in that model and well-conditioned then the banded approximations produce consistent estimates of the eigenvalues and associated eigenvectors of the covariance matrix.
Book
Chance and Stability: Stable Distributions and Their Applications
TL;DR: In this article, the authors introduce the theory of stable laws and apply it to some probabilistic models correlated systems and fractals anomalous diffusion and chaos physics radiophysics astrophysics and cosmology.
Journal ArticleDOI
Large Deviations of Sums of Independent Random Variables
TL;DR: In this article, various variants of bounds for probabilities of large deviations of sums of independent random variables in terms of ordinary and generalized moments of individual summands are discussed. And a great deal of attention is devoted to the study of the precision of these bounds.