Lectures related to Multivariate Statistics: Introduction and Methods

Multivariate Statistics: Normal Distribution

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

Principal Components: Properties & Applications

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

Multivariate Statistics: Normal Distribution

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

Maximum Likelihood Estimation: Multivariate Statistics

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

Multivariate Statistics: Introduction and Methods

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

Copulas: Properties and Applications

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

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 Component Analysis: Properties and Applications

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

Discriminant Analysis: Bayes Rule

Covers the Bayes discriminant rule for allocating individuals to populations based on measurements and prior probabilities.

Principal Component Analysis: Introduction

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

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Canonical Correlation Analysis: Overview

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

Dependence Concepts and Copulas

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

Multivariate Statistics: Conditional Distributions

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

Elliptical Distributions: Properties and Applications

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

Linear Independence: Covariance and Statistical Dependence

Explores covariance, statistical dependence, education-fertility relationship, hypothesis testing, and comparison statistics for continuous outcomes.

Random Vectors & Distribution Functions

Covers random vectors, joint distribution, conditional density functions, independence, covariance, correlation, and conditional expectation.

Elements of Statistics: Probability and Random Variables

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

Dependence in Random Vectors

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

Describing Data: Statistics and Hypothesis Testing

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