# Relaxing the Gaussian assumption in Shrinkage and SURE in high dimension.

@article{Fathi2020RelaxingTG, title={Relaxing the Gaussian assumption in Shrinkage and SURE in high dimension.}, author={Max Fathi and Larry Goldstein and Gesine Reinert and Adrien Saumard}, journal={arXiv: Statistics Theory}, year={2020} }

Shrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon the discovery of his famous paradox. Despite a large subsequent literature, the efficiency of shrinkage, and the associated procedure known as Stein's Unbiased Risk Estimate, or SURE, has mainly been analysed in the Gaussian setting. Importing tools developed for use in the probabilistic area now known as Stein's method, the present work investigates the domain of validity of shrinkage and SURE away…

## 6 Citations

Stein’s Method Meets Statistics: A Review of Some Recent Developments

- Mathematics
- 2021

Stein’s method is a collection of tools for analysing distributional comparisons through the study of a class of linear operators called Stein operators. Originally studied in probability, Stein’s…

High-Dimensional Multi-Task Averaging and Application to Kernel Mean Embedding

- Computer ScienceAISTATS
- 2021

An improved estimator for the multi-task averaging problem, whose goal is the joint estimation of the means of multiple distributions using separate, independent data sets, and it is proved theoretically that this approach provides a reduction in mean squared error.

STEIN’S METHOD OF NORMAL APPROXIMATION: SOME RECOLLECTIONS AND REFLECTIONS BY LOUIS

- Mathematics
- 2021

This paper is a short exposition of Stein’s method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of…

Stein’s method of normal approximation: Some recollections and reflections

- MathematicsThe Annals of Statistics
- 2021

This paper is a short exposition of Stein’s method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of…

Zero Bias Enchanced Stein Couplings

- Mathematics
- 2022

The Stein couplings of Chen and Roellin [6] vastly expanded the range of applications for which coupling constructions in Stein’s method for normal approximation could be applied, and subsumed both…

Stein's Method Meets Computational Statistics: A Review of Some Recent Developments

- Mathematics
- 2021

Stein’s method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical…

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