A First Course in Multivariate Statistics

Front Cover
Springer Science & Business Media, Aug 15, 1997 - Mathematics - 713 pages
2 Reviews
My goal in writing this book has been to provide teachers and students of multi variate statistics with a unified treatment ofboth theoretical and practical aspects of this fascinating area. The text is designed for a broad readership, including advanced undergraduate students and graduate students in statistics, graduate students in bi ology, anthropology, life sciences, and other areas, and postgraduate students. The style of this book reflects my beliefthat the common distinction between multivariate statistical theory and multivariate methods is artificial and should be abandoned. I hope that readers who are mostly interested in practical applications will find the theory accessible and interesting. Similarly I hope to show to more mathematically interested students that multivariate statistical modelling is much more than applying formulas to data sets. The text covers mostly parametric models, but gives brief introductions to computer-intensive methods such as the bootstrap and randomization tests as well. The selection of material reflects my own preferences and views. My principle in writing this text has been to restrict the presentation to relatively few topics, but cover these in detail. This should allow the student to study an area deeply enough to feel comfortable with it, and to start reading more advanced books or articles on the same topic.
 

What people are saying - Write a review

User Review - Flag as inappropriate

Really comprehensive and well presented. shows the beauty of statistics.

User Review - Flag as inappropriate

great book. Straight to the point and Very helpful!

Contents

Why Multivariate Statistics?
1
Exercises for Chapter 1
18
Joint Distribution of Several Random Variables
23
22 Probability Density Function and Distribution Function of a Bivariate Random Variable
25
23 Marginal Distributions
38
24 Independence of Random Variables
47
25 Expected Values Moments Covariance and Correlation
57
26 Conditional Distributions
75
66 UnionIntersection and Likelihood Ratio Testing
418
67 ResamplingBased Testing
435
Discrimination and Classification Round 2
453
Linear vs Quadratic
460
73 Canonical Discriminant Functions
485
74 Multivariate Analysis of Variance
509
75 Simple Logistic Regression
519
76 Multiple Logistic Regression
538

27 Conditional Expectation and Regression
89
28 Mixed DiscreteContinuous Distributions and Finite Mixtures
104
29 Sums of Random Variables
130
210 Notions and Concepts of pvariate Distributions
140
211 Transformations of Random Vectors
155
The Multivariate Normal Distribution
171
32 Definition and Properties of the Multivariate Normal Distribution
175
33 Further Properties of the Multivariate Normal Distribution
186
34 Spherical and Elliptical Distributions
197
Parameter Estimation
209
42 Plugin Estimators
216
43 Maximum Likelihood Estimation
233
44 Maximum Likelihood Estimation with Incomplete Data
260
Discrimination and Classification Round 1
279
52 Standard Distance and the Linear Discriminant Function
280
53 Using the Linear Discriminant Function
302
54 Normal Theory Linear Discrimination
323
55 Error Rates
344
56 Linear Discriminant Functions and Conditional Means
357
Statistical Inference for Means
375
62 The OneSample PTest
377
63 Confidence Regions for Mean Vectors
391
64 The TwoSample Ptest
402
65 Inference for Discriminant Function Coefficients
408
Linear Principal Component Analysis
563
82 SelfConsistent Approximations
568
83 SelfConsistent Projections and Orthogonal Least Squares
578
84 Properties of Linear Principal Components
592
85 Applications
605
86 Sampling Properties
617
87 Outlook
625
Normal Mixtures
639
92 Maximum Likelihood Estimation
645
93 The EMAlgorithm for Normal Mixtures
656
94 Examples
663
Normal Theory Discrimination with Partially Classified Data
679
Selected Results From Matrix Algebra
687
A1 Partitioned Matrices
688
A2 Positive Definite Matrices
689
A3 The Cholesky Decomposition
690
A4 Vector and Matrix Differentiation
691
A5 Eigenvectors and Eigenvalues
692
A6 Spectral Decomposition of Symmetric Matrices
693
A7 The Square Root of a Positive Definite Symmetric Matrix
695
Bibliography
703
Index
711
Copyright

Other editions - View all

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information