Shrinkage estimation of large dimensional precision matrix using random matrix theory
نویسندگان
چکیده
منابع مشابه
Shrinkage Estimation of Large Dimensional Precision Matrix Using Random Matrix Theory
This paper considers ridge-type shrinkage estimation of a large dimensional precision matrix. The asymptotic optimal shrinkage coefficients and the theoretical loss are derived. Data-driven estimators for the shrinkage coefficients are also conducted based on the asymptotic results from random matrix theory. The new method is distribution-free and no assumption on the structure of the covarianc...
متن کاملLinear Ridge Estimator of High-Dimensional Precision Matrix Using Random Matrix Theory
In estimation of the large precision matrix, this paper suggests a new shrinkage estimator, called the linear ridge estimator. This estimator is motivated from a Bayesian aspect for a spike and slab prior distribution of the precision matrix, and has a form of convex combination of the ridge estimator and the identity matrix multiplied by scalar. The optimal parameters in the linear ridge estim...
متن کاملSpectrum estimation for large dimensional covariance matrices using random matrix theory
Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely techniques, in particular in Principal Component Analysis (PCA). In many modern data analysis problems, statisticians are faced with large datasets where the sample si...
متن کاملRandom matrix theory and estimation of high-dimensional covariance matrices
This projects aims to present significant results of random matrix theory in regards to the principal component analysis, including Wigner’s semicircular law and Marčenko-Pastur law describing limiting distribution of large dimensional random matrices. The work bases on the large dimensional data assumptions, where both the number of variables and sample size tends to infinity, while their rati...
متن کاملLarge Dimensional Random Matrix Theory for Signal Detection and Estimation in Array Processing∗
In this paper, we bring into play elements of the spectral theory of large dimensional random matrices and demonstrate their relevance to source detection and bearing estimation in problems with sizable arrays. These results are applied to the sample spatial covariance matrix, R̂, of the sensed data. It is seen that detection can be achieved with a sample size considerably less than that require...
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: Statistica Sinica
سال: 2015
ISSN: 1017-0405
DOI: 10.5705/ss.2012.328