Direct shrinkage estimation of large dimensional precision matrix

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...

Direct Nonlinear Shrinkage Estimation of Large-Dimensional Covariance Matrices

This paper introduces a nonlinear shrinkage estimator of the covariance matrix that does not require recovering the population eigenvalues first. We estimate the sample spectral density and its Hilbert transform directly by smoothing the sample eigenvalues with a variable-bandwidth kernel. Relative to numerically inverting the so-called QuEST function, the main advantages of direct kernel estim...

Nonlinear shrinkage estimation of large-dimensional covariance matrices

Many statistical applications require an estimate of a covariance matrix and/or its inverse. Whenthe matrix dimension is large compared to the sample size, which happens frequently, the samplecovariance matrix is known to perform poorly and may suffer from ill-conditioning. There alreadyexists an extensive literature concerning improved estimators in such situations. In the absence offurther kn...

Approaches to High-Dimensional Covariance and Precision Matrix Estimation

Shrinkage Estimation of the Realized Relationship Matrix

The additive relationship matrix plays an important role in mixed model prediction of breeding values. For genotype matrix X (loci in columns), the product XX' is widely used as a realized relationship matrix, but the scaling of this matrix is ambiguous. Our first objective was to derive a proper scaling such that the mean diagonal element equals 1+f, where f is the inbreeding coefficient of th...