DeepAI AI Chat
Log In Sign Up

Multi-Target Shrinkage

by   Daniel Bartz, et al.

Stein showed that the multivariate sample mean is outperformed by "shrinking" to a constant target vector. Ledoit and Wolf extended this approach to the sample covariance matrix and proposed a multiple of the identity as shrinkage target. In a general framework, independent of a specific estimator, we extend the shrinkage concept by allowing simultaneous shrinkage to a set of targets. Application scenarios include settings with (A) additional data sets from potentially similar distributions, (B) non-stationarity, (C) a natural grouping of the data or (D) multiple alternative estimators which could serve as targets. We show that this Multi-Target Shrinkage can be translated into a quadratic program and derive conditions under which the estimation of the shrinkage intensities yields optimal expected squared error in the limit. For the sample mean and the sample covariance as specific instances, we derive conditions under which the optimality of MTS is applicable. We consider two asymptotic settings: the large dimensional limit (LDL), where the dimensionality and the number of observations go to infinity at the same rate, and the finite observations large dimensional limit (FOLDL), where only the dimensionality goes to infinity while the number of observations remains constant. We then show the effectiveness in extensive simulations and on real world data.


Linear shrinkage of sample covariance matrix or matrices under elliptical distributions: a review

This chapter reviews methods for linear shrinkage of the sample covarian...

Optimal shrinkage covariance matrix estimation under random sampling from elliptical distributions

This paper considers the problem of estimating a high-dimensional (HD) c...

Optimal Eigenvalue Shrinkage in the Semicircle Limit

Recent studies of high-dimensional covariance estimation often assume th...

Mean Shrinkage Estimation for High-Dimensional Diagonal Natural Exponential Families

Shrinkage estimators have been studied widely in statistics and have pro...

Forecasting in Big Data Environments: an Adaptable and Automated Shrinkage Estimation of Neural Networks (AAShNet)

This paper considers improved forecasting in possibly nonlinear dynamic ...

Multi Anchor Point Shrinkage for the Sample Covariance Matrix (Extended Version)

Portfolio managers faced with limited sample sizes must use factor model...

Power Transformations of Relative Count Data as a Shrinkage Problem

Here we show an application of our recently proposed information-geometr...