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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

Description:

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.

Multivariate

statisticsmatt

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#Data Science #Data Analysis #Multivariate Analysis #Programming #Domain-Specific Languages (DSL) #R Programming #Mathematics #Statistics & Probability #Hypothesis Testing #Normal Distribution #Descriptive Statistics #Computer Science #Machine Learning #Dimensionality Reduction #Principal Components Analysis #Linear Discriminant Analysis

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