High Dimensional Covariance Matrix Estimation Shrinkage Toward A Diagonal Target
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High-Dimensional Covariance Matrix Estimation: Shrinkage Toward a Diagonal Target
Author: Mr. Sakai Ando
language: en
Publisher: International Monetary Fund
Release Date: 2023-12-08
This paper proposes a novel shrinkage estimator for high-dimensional covariance matrices by extending the Oracle Approximating Shrinkage (OAS) of Chen et al. (2009) to target the diagonal elements of the sample covariance matrix. We derive the closed-form solution of the shrinkage parameter and show by simulation that, when the diagonal elements of the true covariance matrix exhibit substantial variation, our method reduces the Mean Squared Error, compared with the OAS that targets an average variance. The improvement is larger when the true covariance matrix is sparser. Our method also reduces the Mean Squared Error for the inverse of the covariance matrix.
High-Dimensional Covariance Estimation
Author: Mohsen Pourahmadi
language: en
Publisher: John Wiley & Sons
Release Date: 2013-05-28
Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.
Smooth Forecast Reconciliation
Author: Mr. Sakai Ando
language: en
Publisher: International Monetary Fund
Release Date: 2024-03-22
How to make forecasts that (1) satisfy constraints, like accounting identities, and (2) are smooth over time? Solving this common forecasting problem manually is resource-intensive, but the existing literature provides little guidance on how to achieve both objectives. This paper proposes a new method to smooth mixed-frequency multivariate time series subject to constraints by integrating the minimum-trace reconciliation and Hodrick-Prescott filter. With linear constraints, the method has a closed-form solution, convenient for a high-dimensional environment. Three examples show that the proposed method can reproduce the smoothness of professional forecasts subject to various constraints and slightly improve forecast performance.