Idea Transcript
Help
Contact
RSS
Log in
mathematics and statistics online Search
or
All
Browse by
About
for Researchers
for Librarians
for Publishers
The Annals of Statistics Info
Current issue
All issues
Search
Ann. Statist. Volume 43, Number 4 (2015), 1535-1567.
← Previous article
TOC
Next article Õ
Regularized estimation in sparse high-dimensional time series models
The Institute of Mathematical Statistics
Sumanta Basu and George Michailidis Editorial Board For Authors
Full-text: Access denied (no subscription detected)
Subscriptions
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
First Online Accepted Papers
Buy article
Abstract
Article info and citation
First page
References
Supplemental materials
Abstract Many scientific and economic problems involve the analysis of high-dimensional time series datasets. However, theoretical studies in high-dimensional statistics to date rely primarily on the assumption of independent and identically distributed (i.i.d.) samples. In this work, we focus on stable Gaussian processes and investigate the theoretical properties of -regularized estimates in two important statistical problems in the context of high-dimensional time series: (a) stochastic regression with serially correlated errors and (b) transition matrix estimation in vector autoregressive (VAR) models. We derive nonasymptotic upper bounds on the estimation errors of the regularized estimates and establish that consistent estimation under highdimensional scaling is possible via -regularization for a large class of stable processes under sparsity constraints. A key technical contribution of the work is to introduce a measure of stability for stationary processes using their spectral properties that provides insight into the effect of dependence on the accuracy of the regularized estimates. With this proposed stability measure, we establish some useful deviation bounds for dependent data, which can be used to study several important regularized estimates in a time series setting.
New content alerts Email RSS ToC RSS Article
You have access to this content. You have partial access to this content. You do not have access to this content.
Turn Off MathJax What is MathJax?
More like this Data-driven shrinkage of the spectral density matrix of a high-dimensional time series Fiecas, Mark and von Sachs, Rainer, Electronic Journal of Statistics, 2014 Lasso and probabilistic inequalities for multivariate point processes Hansen, Niels Richard, Reynaud-Bouret, Patricia, and Rivoirard, Vincent, Bernoulli, 2015 Large-sample approximations for variance-covariance matrices of highdimensional time series Steland, Ansgar and von Sachs, Rainer, Bernoulli, 2017 + See more
Browse Accessibility
Search Help
About Contact
Researchers RSS
Librarians
Log in
Publishers
Site feedback
© 2017 Project Euclid