- Tapa blanda: 536 páginas
- Editor: Elsevier Limited; Edición: First Edition, Second Impression (28 de enero de 1980)
- Colección: Probability and Mathematical Statistics
- Idioma: Inglés
- ISBN-10: 0124712525
- ISBN-13: 978-0124712522
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
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nº249.882 en Libros en idiomas extranjeros (Ver el Top 100 en Libros en idiomas extranjeros)
- n.° 471 en Libros en idiomas extranjeros > Ciencias, tecnología y medicina > Matemáticas > Cálculo
- n.° 738 en Libros en idiomas extranjeros > Ciencias, tecnología y medicina > Matemáticas > Estadística y probabilidad
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Multivariate Analysis (Probability and Mathematical Statistics) (Inglés) Tapa blanda – 28 ene 1980
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Multivariate Analysis deals with observations on more than one variable where there is some inherent interdependence between the variables. With several texts already available in this area, one may very well enquire of the authors as to the need for yet another book. Most of the available books fall into two categories, either theoretical or data analytic. The present book not only combines the two approaches but it also has been guided by the need to give suitable matter for the beginner as well as illustrating some deeper aspects of the subject for the research worker. Practical examples are kept to the forefront and, wherever feasible, each technique is motivated by such an example.
Multivariate Analysis deals with observations on more than one variable where there is some inherent interdependence between variables. Most available books on the subject concentrate on either the theoretical or the data analytic approach. This book not only combines theses two approaches but also emphasizes modern developments, so, although primarily designed as a textbook for final year undergraduates and postgraduate students in mathematics and statistics, certain of the sections will commend themselves to research workers.
Broadly speaking the first half of the book contains direct extensions of univariate ideas and techniques, including exploratory data analysis, distribution theory and problems of inference. The remaining chapters concentrate on specifically multivariate problems which have no meaningful analogues in the univariate case. Topics covered include econometrics, principal component analysis, factor analysis, canonical correlation analysis, discriminate analysis, cluster analysis, multi-dimensional scaling and directional data.
Several new methods of presentation are used, for example, the data matrix is emphasized throughout, and density-free approach is given to normal theory, tests are constructed using the likelihood ratio principle and the union intersection principle, and graphical methods are used in explanation.
The reader is assumed to have a basic knowledge of mathematical statistics at an undergraduate level together with an elementary understanding of linear algebra. There are, however, appendices which provide a sufficient background of matrix algebra, a summary of univariate statistics and some statistical tables.
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The reason I did not give if 5 is that it has started to show its age and insists that data is best arranged in rows. Those with a numerical background invariably use columns (unless they are doing funky stuff).
The description of Principal Component Analysis (PCA) is based on eigendecompositions rather than a singular value decomposition. Apart from being a numerical no-no, it is also a nice description of the data.
Every 10-20 years a statistician reinvents a minor variant of PCA (often without obvious knowledge of the previous ones). It would be nice if this was made more explicit. The connection with factor analysis is mentioned (and it has a good chapter of its own), but it would be nice to mention at least the Harkunen-Loeve and Hotelling-transform.