Sample mean and covariance

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Explores covariance, correlation, and mutual information in quantifying statistical dependence between random variables.

Covers Euler and Crank-Nicolson methods for solving differential equations.

Covers Principal Component Analysis for yield curve shape estimation and dimension reduction in interest rate models.

Discusses statistical measures of central tendency and dispersion, focusing on mean, median, and their implications in data analysis.

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

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

Covers the Monte Carlo method for generating realizations and unbiased estimators.

Covers the Power Method for approximating the largest eigenvalue of a matrix.

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