課程專區

• introduction
• review of linear algebra and matrices

• random vectors
• distance
• sample geometry
• random sampling of sample mean vector and covariance matrix
• generalized variance
• matrix operations of sample values

• density and properties
• sampling from multivariate normal and MLE
• sampling distribution and large sample behavior of X and S
• assessing the assumption of normality
• transformation to near normality

• inference for a normal population mean
• Hotelling's T2 and likelihood ratio test
• confidence regions and simultaneous comparisons of component means
• large sample inferences about a population mean vector

• paired comparisons and repeated measures design
• comparing mean vectors from two populations
• comparing several multivariate population means (one-way MANOVA)

• introduction
• population principal components
• summarizing sample variation by principal components
• large sample inferences

• introduction
• orthogonal factor model
• methods of estimation

• factor rotation
• factor scores

• -introduction
• -similarity measures
• -hierarchical clustering methods

•  -k-means clustering methods
•  -model-based clustering
•  -multidimensional scaling　

•  -introduction

Discrimination and classification (2/2)

•  -evaluation of classification functions
•  -classification with several populations
•  -fisher's method for discriminating among several populations

•  -introduction
•  -canonical variates and canonical correlations
•  -interpreting the population canonical variables

•  -sample canonical variates and sample canonical correlations
•  -sample descriptive measures of goodness-of-fit
•  -proportions of explained sample variance
•  -large sample inferences