Covariance Estimation: The GLM and Regularization Perspectives
نویسندگان
چکیده
منابع مشابه
Covariance Estimation: The GLM and Regularization Perspectives
Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent high-dimensional data environment where enforcing the positive-definiteness constraint could be computationally expensive. We provide a survey of the progress made in ...
متن کاملSimultaneous Modelling of Covariance Matrices: GLM, Bayesian and Nonparametric Perspectives
We provide a brief survey of the progress made in modelling covariance matrices from the perspective of generalized linear models (GLM) and the use of link functions (factorizations) that may lead to statistically meaningful and unconstrained reparameterization. We highlight the advantage of the Cholesky decomposition in dealing with the normal likelihood maximization and compare the findings w...
متن کاملCovariance Regularization by Thresholding
This paper considers regularizing a covariance matrix of p variables estimated from n observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense, the variables are Gaussian or sub-Gaussian, and (log p)/n→ 0, and obtain explicit rates. The results are uniform over families of cov...
متن کاملEvaluation and error analysis: Kalman gain regularization versus covariance regularization
Ensemble size is critical to the efficiency and performance of the ensemble Kalman filter, but when the ensemble size is small, the Kalman gain generally cannot be well estimated. To reduce the negative effect of spurious correlations, a regularization process applied on either the covariance or the Kalman gain seems to be necessary. In this paper, we evaluate and compare the estimation errors ...
متن کاملQuantitative covariance NMR by regularization.
The square root of a covariance spectrum, which offers high spectral resolution along both dimensions requiring only few t (1) increments, yields in good approximation the idealized 2D FT spectrum provided that the amount of magnetization exchanged between spins is relatively small. When this condition is violated, 2D FT and covariance peak volumes may differ. A regularization method is present...
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: Statistical Science
سال: 2011
ISSN: 0883-4237
DOI: 10.1214/11-sts358