Moving to Higher Dimensions

Wolfgang Karl Härdle and Leopold Simar
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Wolfgang Karl Härdle: Humboldt-Universität zu Berlin, C.A.S.E. Centre f. Appl. Stat. & Econ. School of Business and Economics

Chapter Chapter 3 in Applied Multivariate Statistical Analysis, 2015, pp 79-115 from Springer

Abstract: Abstract We have seen in the previous chapters how very simple graphical devices can help in understanding the structure and dependency of data. The graphical tools were based on either univariate (bivariate) data representations or on “slick” transformations of multivariate information perceivable by the human eye. Most of the tools are extremely useful in a modelling step, but unfortunately, do not give the full picture of the data set. One reason for this is that the graphical tools presented capture only certain dimensions of the data and do not necessarily concentrate on those dimensions or sub-parts of the data under analysis that carry the maximum structural information. In Part III of this book, powerful tools for reducing the dimension of a data set will be presented. In this chapter, as a starting point, simple and basic tools are used to describe dependency. They are constructed from elementary facts of probability theory and introductory statistics (e.g. the covariance and correlation between two variables).

Keywords: Point Cloud; Linear Regression Model; Matrix Notation; Graphical Tool; Empirical Covariance (search for similar items in EconPapers)
Date: 2015
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Chapter: Moving to Higher Dimensions (2024)
Chapter: Moving to Higher Dimensions (2019)
Chapter: Moving to Higher Dimensions (2003)
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DOI: 10.1007/978-3-662-45171-7_3

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