Multivariate Statistics

Read these first

1. 01Canonical Correlation Analysis

   A way to measure how strongly two whole groups of variables, not just two single variables, move together, by finding the best possible blend of each group to correlate against the other.

2. 02Eigenvalue Clipping and Rotationally Invariant Estimators

   A covariance matrix estimated from finite data has directions of real variance and directions of pure sampling noise mixed together, and eigenvalue clipping is the surgical fix, keep the directions, correct the sizes.

3. 03Hotelling's T-Squared Test

   The multivariate version of the t-test, it checks whether a whole vector of measurements has shifted from what you expected, in a way that properly accounts for how those measurements move together.

4. 04Mahalanobis Distance and Multivariate Outliers

   A way of measuring distance that accounts for correlation, so a data point can be flagged as a genuine outlier even when it looks perfectly ordinary on every variable taken one at a time.

Then the rest

1. 05Archimedean Copulas: Clayton, Gumbel and Frank
2. 06Choosing a Covariance Shrinkage Target
3. 07Covariance Estimation With Unequal History
4. 08Distance and Similarity Measures for Assets
5. 09Exponentially Weighted Covariance and Half-Life Choice
6. 10Horn's Parallel Analysis
7. 11MANOVA and Wilks' Lambda
8. 12Multidimensional Scaling
9. 13Quadratic and Regularized Discriminant Analysis
10. 14Reduced-Rank Regression
11. 15The Graphical Lasso and Sparse Precision Matrices
12. 16The Sample Covariance Matrix and Eigenvalue Bias
13. 17Vine Copulas for High-Dimensional Dependence