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Certain types of problems involving multivariate data, for example simple linear regression and multiple regression, are not usually considered to be special cases of multivariate statistics because the analysis is dealt with by considering the (univariate) conditional distribution of a single outcome variable given the other variables.
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]
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]
Multivariate Kernel Smoothing and Its Applications is a comprehensive book on many topics in kernel smoothing, including density estimation. Includes ks package code snippets in R . kde2d.m A Matlab function for bivariate kernel density estimation.
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.
Formally, a multivariate random variable is a column vector = (, …,) (or its transpose, which is a row vector) whose components are random variables on the probability space (,,), where is the sample space, is the sigma-algebra (the collection of all events), and is the probability measure (a function returning each event's probability).
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:
Download as PDF; Printable version; ... Multivariate is the quality of having multiple variables. ... Multivariate analysis;