MVNtestchar-package: Test for Multivariate Normal Distribution Based on a...

In MVNtestchar: Test for Multivariate Normal Distribution Based on a Characterization

Description

Provides a test of multivariate normality of an unknown sample that does not require estimation of the nuisance parameters, the mean and covariance matrix. Rather, a sequence of transformations removes these nuisance parameters and results in a set of sample matrices that are positive definite. These matrices are uniformly distributed on the space of positive definite matrices in the unit hyper-rectangle if and only if the original data is multivariate normal (Fairweather, 1973, Doctoral dissertation, University of Washington). The package performs a goodness of fit test of this hypothesis. In addition to the test, functions in the package give visualizations of the support region of positive definite matrices for bivariate samples.

Details

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Provides a test of multivariate normality of a sample which does not require estimation of the nuisance parameters, the mean vector and covariance matrix. Rather, a sequence of transformations removes these nuisance parameters, resulting in a set of sample matrices that are positive definite. If, and only if the original data is multivariate normal, these matrices are uniformly distributed on the space of positive definite matrices in the unit hyper-rectangle. The package performs a goodness of fit test of this hypothesis. In addition to the test, functions in the package give visualizations of the support region of positive definite matrices for p equals 2.

Author(s)

person("Fairweather", "William", email = "[e-mail]", role = c("aut", "cre"))

References

Anderson, TW. (1958), An Introduction to Multivariate Statistical Analysis, John Wiley, New York.

Cramer, H (1962). Random Variables and Probability Distributions, Cambridge University Press, London.

Csorgo M and Seshadri V (1970). On the problem of replacing composite hypotheses by equivalent simple ones, Rev. Int. Statist. Instit., 38, 351-368

Csorgo M and Seshadri V (1971). Characterizing the Gaussian and exponential laws by mappings onto the unit interval, Z. Wahrscheinlickhkeitstheorie verw. Geb., 18, 333-339

Deemer,WL and Olkin,I (1951). The Jacobians of certain matrix transformations useful in multivariate analysis, *Biometrika*, **58**, 345 367.

Fairweather WR (1973). A test for multivariate normality based on a characterization. Dissertation submitted in partial fulfillment of the requirements for the Doctor of Philosophy, University of Washington, Seattle WA

MVNtestchar documentation built on July 26, 2020, 1:07 a.m.