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Interactive Graphics for Data Analysis. Malakooti, B. (2013). Operations and Production Systems with Multiple Objectives. John Wiley & Sons. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley, New York, 1958. KV Mardia; JT Kent & JM Bibby (1979). Multivariate Analysis. Academic Press. ISBN 978-0124712522.
Anderson's 1958 [3] textbook, An Introduction to Multivariate Analysis, [4] educated a generation of theorists and applied statisticians; Anderson's book emphasizes hypothesis testing via likelihood ratio tests and the properties of power functions: Admissibility, unbiasedness and monotonicity. [5] [6]
In statistics, particularly in hypothesis testing, the Hotelling's T-squared distribution (T 2), proposed by Harold Hotelling, [1] is a multivariate probability distribution that is tightly related to the F-distribution and is most notable for arising as the distribution of a set of sample statistics that are natural generalizations of the statistics underlying the Student's t-distribution.
The probability content of the multivariate normal in a quadratic domain defined by () = ′ + ′ + > (where is a matrix, is a vector, and is a scalar), which is relevant for Bayesian classification/decision theory using Gaussian discriminant analysis, is given by the generalized chi-squared distribution. [17]
Statistical analyses of multivariate data often involve exploratory studies of the way in which the variables change in relation to one another and this may be followed up by explicit statistical models involving the covariance matrix of the variables. Thus the estimation of covariance matrices directly from observational data plays two roles:
The goal of density estimation is to take a finite sample of data and to make inferences about the underlying probability density function everywhere, including where no data are observed. In kernel density estimation, the contribution of each data point is smoothed out from a single point into a region of space surrounding it.