Dependence Concepts and Copulas

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Related lectures (31)

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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.