Lectures related to Covariance matrix

Principal Components: Properties & Applications

Explores principal components, covariance, correlation, choice, and applications in data analysis.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Shrinkage Estimation of Large Covariance Matrices

Explores shrinkage estimation of high-dimensional covariance matrices, comparing linear and nonlinear approaches for improved accuracy.

Multivariate Statistics: Normal Distribution

Covers the multivariate normal distribution, properties, and sampling methods.

Principal Component Analysis: Dimension Reduction

Covers Principal Component Analysis for dimension reduction in biological data, focusing on visualization and pattern identification.

Market Response Functions

Explores market response functions, flash crashes, correlation estimation, and noise filtering in finance.

Dependence in Random Vectors

Explores dependence in random vectors, covering joint density, conditional independence, covariance, and moment generating functions.

VaR Model Evaluation

Discusses Monte Carlo VaR accuracy, confidence intervals, backtesting, and multivariate distributions.

PCA: Derivation and Optimization

Covers the derivation of PCA projection, error minimization, and eigenvector optimization.

Covariance Cleaning and Estimators

Explores covariance matrix cleaning, optimal estimators, and rotationally invariant methods for portfolio optimization.

Estimating R: Moments and Covariance

Covers the estimation of R, focusing on moments and covariance.

Principal Component Analysis: Understanding Data Structure

Explores Principal Component Analysis, dimensionality reduction, data quality assessment, and error rate control.

Quantifying Statistical Dependence: Covariance and Correlation

Explores covariance, correlation, and mutual information in quantifying statistical dependence between random variables.

Linear Dimensionality Reduction

Explores linear dimensionality reduction through PCA, variance maximization, and real-world applications like medical data analysis.

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Multivariate Statistics: Introduction and Methods

Introduces multivariate statistics, focusing on uncovering associations between components in data in vector form.

Max-Stable Models: Smith and Schlather

Covers the Smith and Schlather max-stable models, exploring their validity and interpretation.

Principal Component Analysis: Theory and Applications

Covers the theory and applications of Principal Component Analysis, focusing on dimension reduction and eigenvectors.

Non-Negative Definite Matrices and Covariance Matrices

Covers non-negative definite matrices, covariance matrices, and Principal Component Analysis for optimal dimension reduction.

Principal Component Analysis: Covariance Matrix and Eigenvalues

Explores Principal Component Analysis focusing on maximizing variance and finding eigenvalues.