General Linear Models - Background Material

General Linear Models - Background Material

statisticsmatt via YouTube Direct link

Random Vectors and Random Matrices

1 of 25

1 of 25

Random Vectors and Random Matrices

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General Linear Models - Background Material

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  1. 1 Random Vectors and Random Matrices
  2. 2 Statistical Distributions: Central & Noncentral t Distributions
  3. 3 Statistical Distributions: Central & Noncentral Chi square df=1 Distributions
  4. 4 Statistical Distributions: Derive the F Distribution
  5. 5 Statistical Distributions: NonCentral F Distribution
  6. 6 Idempotent Matrices
  7. 7 Independence of Quadratic Forms
  8. 8 Independence of Quadratic Forms (another proof)
  9. 9 Distribution of quadratic form n(xbar-mu)Sigma(xbar-mu), where x~MVN(mu,sigma)
  10. 10 Distribution of Quadratic Forms (part 1)
  11. 11 Distribution of Quadratic Forms (part 2)
  12. 12 Distribution of Quadratic Forms (part 3)
  13. 13 (1-a)% Confidence Region for a multivariate mean vector when the data are multivariate normal
  14. 14 Derivative of a Quadratic Form with respect to a Vector
  15. 15 Projection Matrices: Introduction
  16. 16 Perpendicular Projection Matrix
  17. 17 Mean, Variance, and Covariance of Quadratic Forms
  18. 18 A Square-Root Matrix
  19. 19 Inverse of a Partitioned Matrix
  20. 20 The Spectral Decomposition (Eigendecomposition)
  21. 21 Woodbury Matrix Identity & Sherman-Morrison Formula
  22. 22 Generalized Inverse Matrix
  23. 23 Generalized Inverse for a Symmetric Matrix
  24. 24 Gram-Schmidt Orthonormalization Process: Perpendicular Projection Matrix
  25. 25 Sum of Perpendicular Projection Matrices

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