A unified approach for covariance matrix estimation under Stein loss
نویسندگان
چکیده
In this paper, we address the problem of estimating a covariance matrix multivariate Gaussian distribution, relative to Stein loss function, from decision theoretic point view. We investigate case where is invertible and when it non--invertible in unified approach.
منابع مشابه
Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions
Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or even larger. In such settings, there is a common remedy for both statistical problems: nonlinear shrinkage of the eigenvalues of the sample covariance matrix. T...
متن کاملOptimal estimation of a large-dimensional covariance matrix under Stein's loss
This paper revisits the methodology of Stein (1975, 1986) for estimating a covariance matrix in the setting where the number of variables can be of the same magnitude as the sample size. Stein proposed to keep the eigenvectors of the sample covariance matrix but to shrink the eigenvalues. By minimizing an unbiased estimator of risk, Stein derived an ‘optimal’ shrinkage transformation. Unfortuna...
متن کاملEstimation of Covariance Matrix
Estimation of population covariance matrices from samples of multivariate data is important. (1) Estimation of principle components and eigenvalues. (2) Construction of linear discriminant functions. (3) Establishing independence and conditional independence. (4) Setting confidence intervals on linear functions. Suppose we observed p dimensional multivariate samples X1, X2, · · · , Xn i.i.d. wi...
متن کاملAdaptive Thresholding for Sparse Covariance Matrix Estimation
In this article we consider estimation of sparse covariance matrices and propose a thresholding procedure that is adaptive to the variability of individual entries. The estimators are fully data-driven and demonstrate excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covarianc...
متن کاملCovariance Matrix Estimation for Reinforcement Learning
One of the goals in scaling reinforcement learning (RL) pertains to dealing with high-dimensional and continuous stateaction spaces. In order to tackle this problem, recent efforts have focused on harnessing well-developed methodologies from statistical learning, estimation theory and empirical inference. A key related challenge is tuning the many parameters and efficiently addressing numerical...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2022
ISSN: ['1631-073X', '1778-3569']
DOI: https://doi.org/10.5802/crmath.356