Merge branch 'main' of https://github.com/microprediction/precise

Author: microprediction

Diff for: LITERATURE.md

@@ -7,6 +7,24 @@ In no particular order. The scope is robust diversified portfolios and things th
 Or file an [issue](https://github.com/microprediction/precise/issues).  
 
 
+## Regularized Tyler’s Scatter Estimator: Existence, Uniqueness, and Algorithms [pdf](https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6879466)
+Ying Sun and Daniel P. Palomar
+
+This paper considers the regularized Tyler’s scatter
+estimator for elliptical distributions, which has received considerable attention recently. Various types of shrinkage Tyler’s estimators have been proposed in the literature and proved work effectively in the “large small ” scenario. Nevertheless, the existence
+and uniqueness properties of the estimators are not thoroughly
+studied, and in certain cases the algorithms may fail to converge.
+In this work, we provide a general result that analyzes the sufficient condition for the existence of a family of shrinkage Tyler’s
+estimators, which quantitatively shows that regularization indeed
+reduces the number of required samples for estimation and the
+convergence of the algorithms for the estimators. For two specific
+shrinkage Tyler’s estimators, we also proved that the condition is
+necessary and the estimator is unique. Finally, we show that the
+two estimators are actually equivalent. Numerical algorithms are
+also derived based on the majorization-minimization framework,
+under which the convergence is analyzed systematically.
+
+
 ## James–Stein for the leading eigenvector [pdf](https://www.pnas.org/doi/epdf/10.1073/pnas.2207046120)
 Lisa Goldberg and Alec Kercheval
 

Diff for: README.md

@@ -1,8 +1,8 @@
 # precise [docs](https://microprediction.github.io/precise/) ![tests](https://github.com/microprediction/precise/workflows/tests/badge.svg) ![tests-scipy-173](https://github.com/microprediction/precise/workflows/tests-scipy-173/badge.svg) ![tests-sans-ppo](https://github.com/microprediction/precise/workflows/tests-sans-ppo/badge.svg)  ![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)
 
-Goals:
+Contents:
 
-1. A collection of *online* [covariance forecasting](https://github.com/microprediction/precise/blob/main/LISTING_OF_COV_SKATERS.md) and [portfolio construction](https://github.com/microprediction/precise/blob/main/LISTING_OF_MANAGERS.md) functions. See [docs](https://microprediction.github.io/precise/). 
+1. A collection of *online* (incremental) [covariance forecasting](https://github.com/microprediction/precise/blob/main/LISTING_OF_COV_SKATERS.md) and [portfolio construction](https://github.com/microprediction/precise/blob/main/LISTING_OF_MANAGERS.md) functions. See [docs](https://microprediction.github.io/precise/). 
 
 2. "Schur Complementary" portfolio construction, a new approach that leans on connection between top-down (hierarchical) and bottom-up (optimization) portfolio construction revealed by block matrix inversion. See my posts on the [methodology](https://www.linkedin.com/posts/petercotton_schur-complementary-portfolios-a-unification-activity-7000535020381552640-ZWej?utm_source=share&utm_medium=member_desktop) and its role in the [hijacking of the M6 contest](https://www.linkedin.com/posts/alexander-fleiss-70b49410_does-option-volume-predict-stock-direction-activity-7021134433344749569-bxx4?utm_source=share&utm_medium=member_desktop). 
 

Diff for: examples_portfolios/m6/README.md

@@ -1,6 +1,8 @@
 
 ## M6 Financial forecasting contest utilities
 
+Warning ... this is no longer maintained. 
+
 You can use this library to enter M6 as follows:
 
    1. Pick a cov estimator (i.e. a "cov skater"), if you wish