Covariance Matrix Estimation in Time Series

Wu, Wei Biao; Xiao, Han

doi:10.1016/b978-0-444-53858-1.00008-9

Cited by 17 publications

(15 citation statements)

References 69 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Parameters of autoregressive moving average processes are estimated either by Yule-Walker or maximum likelihood estimators, both attaining parametric rates. Another approach is to band or taper the empirical autocovariance function of y (Bickel & Levina, 2008;Wu & Pourahmadi, 2009;Wu & Xiao, 2012). These nonparametric estimators are very flexible, but are computationally intensive and have slower convergence rates.…”

Section: ·2 Estimation Of Covariance Matricesmentioning

confidence: 99%

Partial least squares for dependent data

et al. 2016

View full text Add to dashboard Cite

show abstract

Section: ·2 Estimation Of Covariance Matricesmentioning

confidence: 99%

Partial least squares for dependent data

et al. 2016

View full text Add to dashboard Cite

show abstract

“…While Proposition 2 has R positive definite with probability tending to one, in finite-sample situations, R may not be. To obtain positive-definite estimates, several modification methods have been proposed (e.g., ; Wu and Xiao (2011); ; Zhang and Yu (2008)). and Zhang and Yu (2008) proposed a positive-definite estimate of R −1 by refining R −1 .…”

Section: Theoretical Resultsmentioning

confidence: 99%

Estimation of the error autocorrelation matrix in semiparametric model for fMRI data

Guo¹,

Zhang²

2015

STAT SINICA

View full text Add to dashboard Cite

In statistical analysis of functional magnetic resonance imaging (fMRI), dealing with the temporal correlation is a major challenge in assessing changes within voxels. This paper aims to address this issue by considering a semiparametric model for single-voxel fMRI. For the error process in the semiparametric model with autocorrelation matrix R, we adopt the difference-based method to construct a banded estimate R of R, and propose a refined estimate R −1 * of R −1. Under mild regularity conditions, we establish consistency of R and R * with explicit convergence rates. We also demonstrate convergence of R −1 * in mean square under the L∞ norm, though this convergence property does not hold for R −1. Datadriven procedures for choosing the banding parameter and refining the estimate are developed, and simulation studies reveal their satisfactory performance. Numerical results suggest that R −1 * performs well when applied to the semiparametric test statistics for detecting brain activity.

show abstract

“…Linear Gaussian covariance models were introduced by Anderson (), motivated by the linear structure of covariance matrices in various time series models, and have been used more recently for the analysis of repeated time series and longitudinal data (Pourahmadi, ; Jansson and Ottersten, ; Wu and Xiao, ). Anderson proposed iterative procedures for calculating the maximum likelihood estimator (MLE) of

Σ_{v}

, such as the Newton–Raphson method (Anderson, ) and a scoring method (Anderson, ).…”

Section: Introductionmentioning

confidence: 99%

Maximum Likelihood Estimation for Linear Gaussian Covariance Models

Zwiernik

Uhler

Richards

2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

View full text Add to dashboard Cite

We study parameter estimation in linear Gaussian covariance models, which are p-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex optimization problem which typically has many local maxima. Using recent results on the asymptotic distribution of extreme eigenvalues of the Wishart distribution, we provide sufficient conditions for any hill-climbing method to converge to the global maximum. Although we are primarily interested in the case in which n > > p, the proofs of our results utilize large-sample asymptotic theory under the scheme n/p → γ > 1. Remarkably, our numerical simulations indicate that our results remain valid for p as small as 2. An important consequence of this analysis is that for sample sizes n 14p, maximum likelihood estimation for linear Gaussian covariance models behaves as if it were a convex optimization problem.1. Introduction. In many statistical analyses, the covariance matrix possesses a specific structure and must satisfy certain constraints. We refer to [Pou11] for a comprehensive review of covariance estimation in general and a discussion of numerous specific covariance matrix constraints. In this paper, we study Gaussian models with linear constraints on the covariance matrix. Simple examples of such models are correlation matrices or covariance matrices with prescribed zeros.Linear Gaussian covariance models appear in various applications. They were introduced to study repeated time series [And70] and are used in various engineering problems [ZC05,Die07]. In Section 2, we describe in detail Brownian motion tree models, a particular class of linear Gaussian covariance models, and their applications to phylogenetics and network tomography.To define Gaussian models with linear constraints on the covariance matrix, let S p be the set of symmetric p × p matrices considered as a subset of

show abstract

Covariance Matrix Estimation in Time Series

Cited by 17 publications

References 69 publications

Partial least squares for dependent data

Partial least squares for dependent data

Estimation of the error autocorrelation matrix in semiparametric model for fMRI data

Maximum Likelihood Estimation for Linear Gaussian Covariance Models

Contact Info

Product

Resources

About