Lectures related to Multivariate Statistics: Normal Distribution

Multivariate Statistics: Normal Distribution

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

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.

Copulas: Properties and Applications

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

Maximum Likelihood Estimation: Multivariate Statistics

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

Principal Component Analysis: Introduction

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

Canonical Correlation Analysis: Overview

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

Multivariate Statistics: Introduction and Methods

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

Multivariate Statistics: Conditional Distributions

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

Dependence in Random Vectors

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

Elements of Statistics

Introduces key statistical concepts like probability, random variables, and correlation, with examples and explanations.

Dependence Concepts and Copulas

Explores dependence concepts, copulas, correlation fallacies, and rank correlations in statistics.

Central Limit Theorem: Properties and Applications

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

Multivariate Normal Distribution

Covers the multivariate normal distribution, moment-generating function, and combinatorics.

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Multivariate Statistics: Introduction and Methods

Introduces major statistical methodologies for uncovering associations between vector components in multivariate data.

Linear Combinations: Moment-Generating Functions

Explores moment-generating functions, linear combinations, and normality of random variables.

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Dependence and Correlation

Explores dependence, correlation, and conditional expectations in probability and statistics, highlighting their significance and limitations.

Probability and Statistics

Covers probability, statistics, independence, covariance, correlation, and random variables.