WJWJ Maths
Multivariate Statistical Analysis
  • Review of Matrix Algebra
  • Matrix
  • Vector
  • Some Particular Matrices
  • Basic Matrix Operations
  • Further Matrices
  • Orthogonal Matrices
  • Centering Matrix
  • Vectors and Matrices
  • Spectral Decomposition
  • Practice Problems
  • Basic Properties of Random Vectors
  • Marginal and Conditional Distribution Functions
  • Independence
  • Population Moments
  • Conditional Moments
  • Correlation Matrix
  • Practice Problems
  • Introduction To Multivariate Data
  • Introduction
  • Data Matrix
  • Summary Statistics
  • Measures of Multivariate Scatter
  • Geometrical Ideals
  • Practice Problems
  • Principal Component Analysis
  • Population Principal Components
  • How Much Variation Each Component Explains
  • Components from the Correlation Matrix
  • Sample Principal Components
  • How Many Components to Keep
  • Practice Problems
  • The Multivariate Normal Distribution
  • Definition and Basic Properties
  • Sampling from a Multivariate Normal Population
  • The Wishart Distribution
  • Hotellings
  • Wilks Lambda
  • Confidence Regions
  • Comparison of Two Multivariate Means
  • Paired Comparisons
  • Two Independent Samples
  • Simultaneous Confidence Statements
  • Practice Problems
  • Classification and Discrimination
  • Fisher’s Discriminant Function
  • Fishers Classification Rule
  • Fishers Rule Through Mahalanobie’s Distance
  • More Than Two Population
  • Sample Values
  • Fishers Sample Linear Discriminate
  • Fishers Classification Procedure Based of On Sample Discriminate
  • Practice Problems
  • Multivariate Analysis of Variance (MANOVA)
  • Incorporating Data
  • Two-Way MANOVA
  • Practice Problems
  • Multivariate Multiple Regression
  • The Model and Its Notation
  • Least Squares Estimation
  • Fitted Values and Residuals
  • References
  • Practice Problems
  • Factor Analysis
  • The Orthogonal Factor Model
  • Non-uniqueness and Rotation
  • Estimation
  • Practice Problems
  • Canonical Correlation Analysis
  • Canonical Variates
  • Solution by Eigenvalues
  • Special Cases and Cautions
  • Practice Problems
  • Cluster Analysis
  • Distance
  • Hierarchical Methods
  • \(k\)-Means
  • Practice Problems

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3 Introduction To Multivariate Data

3.1 Introduction
3.2 Data Matrix
3.3 Summary Statistics
3.3.1 The Mean Vector and Covariance Matrix
3.3.2 Correlation Matrix
3.4 Measures of Multivariate Scatter
3.5 Geometrical Ideals
3.5.1 R-Techniques
3.5.2 Q-Techniques
3.5.3 Univariate Scatters
3.5.4 Linear Combinations
3.6 Practice Problems

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