Explore advanced multivariate statistical concepts and techniques in this comprehensive 6-hour tutorial series. Delve into topics such as multivariate sign tests, bivariate normal distributions, linear discriminant analysis, and quadratic forms. Learn to apply R programming for calculating probabilities, conducting tests, and determining power and sample sizes. Investigate statistical distance, Gaussian integrals, and spherical coordinates. Examine multivariate normal distributions, confidence regions, and descriptive statistics. Study advanced topics like Follmann's test for comparing treatment arms and dose escalation hypotheses. Gain insights into covariance, random vectors, and matrices. Conclude with an in-depth exploration of principal component analysis, covering background, derivation, explained variance, and correlation.
Overview
Syllabus
A Simple Multivariate Test for One Sided Alternatives.
The Multivariate Sign Test.
Probability of 1st Quadrant for a Scaled Bivariate Normal Random Variable.
Using R: Calculating Probability for a Bivariate Normal Random Variable.
Using R: The Multivariate Sign Test.
Power and Sample Size in R: Multivariate Sign Test.
Statistical Distance.
A Square-Root Matrix.
Extended Cauchy-Schwarz Inequality.
Linear Discriminant Analysis.
Distribution of Quadratic Forms (part 1).
Distribution of Quadratic Forms (part 2).
Distribution of Quadratic Forms (part 3).
Gaussian Integrals.
Spherical Coordinates.
Multivariate Normal Random Variable transformed to a Multivariate Uniform Random Variable.
Rotational Invariance.
(1-a)% Confidence Region for a multivariate mean vector when the data are multivariate normal.
Multivariate Descriptive Statistics.
Multivariate Normal Distribution as an approximation to the Multinomial Distribution.
Testing all Treatments Arms against a Control Arm using Follmann's Test.
Dose Escalation Hypotheses Testing using Follmann's Test.
Using R to test multivariate ordered alternatives with Follmann's test.
Cov(y1, y2)=0 if and only if (y1 independent of y2).
Random Vectors and Random Matrices.
Principal Components (part 1): Background.
Principal Components (part 2): Derivation.
Principal Components (part 3): "Explained" Variance.
Principal Components (part 4): Correlation.
Taught by
statisticsmatt
