Lectures related to Estimation of covariance matrices

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.

Principal Components: Properties & Applications

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

Shrinkage Estimation of Large Covariance Matrices

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

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: Dimension Reduction

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

Principal Component Analysis: Properties and Applications

Explores Principal Component Analysis theory, properties, applications, and hypothesis testing in multivariate statistics.

Multivariate Statistics: Normal Distribution

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

Multivariate Statistics: Normal Distribution

Introduces multivariate statistics, covering normal distribution properties and characteristic functions.

Multivariate Statistics: Introduction and Methods

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

Dependence in Random Vectors

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

Maximum Likelihood Theory & Applications

Covers maximum likelihood theory, applications, and hypothesis testing principles in econometrics.

Gaussian Correlation Conjecture

Explores the proof of the Gaussian correlation conjecture and its implications on random vectors and covariance matrices.

Classification with GMM and kNN

Covers classification using GMM and kNN, exploring boundaries, errors, and practical exercises.

Gaussian Random Vectors: Conditional Generation

Explores generating Gaussian random vectors with specific components based on observed values and explains the concept of positive definite covariance functions in Gaussian processes.

Quantifying Statistical Dependence: Covariance and Correlation

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

Joint Distribution of Gaussian Random Vectors

Explores the criteria for Gaussian random vectors to have a joint PDF.

Principal Component Analysis: Theory and Applications

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

Principal Component Analysis: Understanding Data Structure

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

Covariance Cleaning and Estimators

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

Optimization in Statistics and Machine Learning: Maximum Likelihood Estimation

Explores Maximum Likelihood Estimation, linear models, logistic regression, and Support Vector Machines.