Lectures related to Shrinkage Estimation of Large Covariance Matrices

Principal Components: Properties & Applications

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

Principal Component Analysis: Theory and Applications

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

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

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.

Multivariate Statistics: Introduction and Methods

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

Optimality in Decision Theory: Unbiased Estimation

Explores optimality in decision theory and unbiased estimation, emphasizing sufficiency, completeness, and lower bounds for risk.

Dependence in Random Vectors

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

Maximum Likelihood Estimation

Explores Maximum Likelihood Estimation, covering assumptions, properties, distribution, shrinkage estimation, and loss functions.

Covariance Cleaning and Estimators

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

Eigenstate Thermalization Hypothesis

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

The Stein Phenomenon and Superefficiency

Explores the Stein Phenomenon, showcasing the benefits of bias in high-dimensional statistics and the superiority of the James-Stein Estimator over the Maximum Likelihood Estimator.

Statistical Theory: Maximum Likelihood Estimation

Explores the consistency and asymptotic properties of the Maximum Likelihood Estimator, including challenges in proving its consistency and constructing MLE-like estimators.

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.

Causal Systems & Transforms: Delay Operator Interpretation

Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.

Elements of Statistics: Probability, Distributions, and Estimation

Covers probability theory, distributions, and estimation in statistics, emphasizing accuracy, precision, and resolution of measurements.

Maximum Likelihood Theory & Applications

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

Monte Carlo: Markov Chains

Covers unsupervised learning, dimensionality reduction, SVD, low-rank estimation, PCA, and Monte Carlo Markov Chains.

Multivariate Statistics: Normal Distribution

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

Estimators and Confidence Intervals

Explores bias, variance, unbiased estimators, and confidence intervals in statistical estimation.