Explore essential background material for understanding General Linear Models in this comprehensive video playlist. Delve into topics such as random vectors and matrices, statistical distributions, idempotent matrices, quadratic forms, confidence regions, projection matrices, and matrix algebra. Begin with the General Linear Models: Regression playlist and refer back to this background material as needed to deepen your understanding of key concepts and mathematical foundations.
Overview
Syllabus
Random Vectors and Random Matrices.
Statistical Distributions: Central & Noncentral t Distributions.
Statistical Distributions: Central & Noncentral Chi square df=1 Distributions.
Statistical Distributions: Derive the F Distribution.
Statistical Distributions: NonCentral F Distribution.
Idempotent Matrices.
Independence of Quadratic Forms.
Independence of Quadratic Forms (another proof).
Distribution of quadratic form n(xbar-mu)Sigma(xbar-mu), where x~MVN(mu,sigma).
Distribution of Quadratic Forms (part 1).
Distribution of Quadratic Forms (part 2).
Distribution of Quadratic Forms (part 3).
(1-a)% Confidence Region for a multivariate mean vector when the data are multivariate normal.
Derivative of a Quadratic Form with respect to a Vector.
Projection Matrices: Introduction.
Perpendicular Projection Matrix.
Mean, Variance, and Covariance of Quadratic Forms.
A Square-Root Matrix.
Inverse of a Partitioned Matrix.
The Spectral Decomposition (Eigendecomposition).
Woodbury Matrix Identity & Sherman-Morrison Formula.
Generalized Inverse Matrix.
Generalized Inverse for a Symmetric Matrix.
Gram-Schmidt Orthonormalization Process: Perpendicular Projection Matrix.
Sum of Perpendicular Projection Matrices.
Taught by
statisticsmatt
