Lectures related to Dependence Concepts and Copulas

Copulas: Properties and Applications

Explores copulas in multivariate statistics, covering properties, fallacies, and applications in modeling dependence structures.

Principal Component Analysis: Introduction

Introduces Principal Component Analysis, focusing on maximizing variance in linear combinations to summarize data effectively.

Multivariate Statistics: Normal Distribution

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

Describing Data: Statistics and Hypothesis Testing

Covers descriptive statistics, hypothesis testing, and correlation analysis with various probability distributions and robust statistics.

Copulas: Dependence Modeling

Covers copulas, Sklar's Theorem, types of copulas, and simulation of copulas for risk management.

Canonical Correlation Analysis: Overview

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Copulas: Dependence Structures and Simulation

Covers copulas, dependence structures, simulation techniques, and properties of copula densities.

Principal Components: Properties & Applications

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

Copulas: Properties and Applications

Covers copulas, Sklar's Theorem, meta distributions, and various dependence measures like rank correlations and coefficients of tail dependence.

Dependence Measures: Rank Correlations

Covers rank correlations, tail dependence, and copula fitting methods.

Multivariate Statistics: Normal Distribution

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

Multivariate Normal Distribution: Correlation and Covariance

Covers correlation, covariance, empirical estimates, eigenvalues, normality testing, and factor models.

Elliptical Distributions: Properties and Applications

Covers elliptical distributions, including properties, applications, and risk management implications.

Maximum Likelihood Estimation: Multivariate Statistics

Explores maximum likelihood estimation and multivariate hypothesis testing, including challenges and strategies for testing multiple hypotheses.

Copulas and Tail Dependence

Explores copulas, rank correlations, and tail dependence measures in risk management.

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: Conditional Distributions

Covers conditional distributions and correlations in multivariate statistics, including partial variance and covariance, with applications to non-normal distributions.

Red bus/Blue bus paradox

Explores the Red bus/Blue bus paradox, nested logit models, and multivariate extreme value models in transportation.

Central Limit Theorem: Properties and Applications

Explores the Central Limit Theorem, covariance, correlation, joint random variables, quantiles, and the law of large numbers.

Causal Systems & Transforms: Delay Operator Interpretation

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