A First Course in Multivariate StatisticsMy 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. |
Contents
| 23 | |
The Multivariate Normal Distribution | 171 |
Parameter Estimation 209 | 208 |
Discrimination and Classification Round 1 | 279 |
Statistical Inference for Means | 375 |
Discrimination and Classification Round 2 | 453 |
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Common terms and phrases
assume B₁ bivariate normal chi-square classification rule coefficients compute conditional distribution continuation of Example correlation Cov[X defined degrees of freedom denote density function dimension eigenvalues eigenvectors EM-algorithm equal error rate Figure follows fx(x given graph Hint hypothesis independent joint distribution joint pdf likelihood function linear combination linear discriminant function log-likelihood function log-likelihood ratio log-likelihood ratio statistic logistic regression marginal distribution maximum likelihood estimates mean vector midge mixture density multivariate normal multivariate normal distribution N₁ N₂ normal distribution normal mixture normal theory optimal classification orthogonal p-variate random vector p₁ partitioned plug-in positive definite posterior probabilities Pr[X prior probabilities probability function random variable random vector sample covariance matrix scatterplot self-consistent setup Show standard errors Suppose symmetric Table Theorem transformation univariate var[Y variance wing length X₁ Y₁ Y₂ zero μ₁ μι