S2.test: Chi-squared type tests for Multivariate Normality
In mvnTest: Goodness of Fit Tests for Multivariate Normality

Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/S2.test.r

This function implements three chi-squared type goodness-of-fit tests for multivariate normality, namely, the McCulloch S2 test, Nikulin-Rao-Robson Y2 and Dzhaparidze-Nikulin U2 tests.

1	S2.test(data, M=5, qqplot = FALSE)

`data`	A numeric matrix or data frame
`M`	A number of equiprobable intervals
`qqplot`	if `TRUE` it creates a chi-square Q-Q plot

Calculates the values of the three chi-squared type test statistics, the McCulloch S2, Nikulin-Rao-Robson Y2 and Dzhaparidze-Nikulin U2 tests, and the corresponding p-values. The construction of all three tests is based on the Wald's type chi-squared goodness-of-fit tests. The vector of unknown parameters is estimated by the maximum likelihood method.The Karhunen-Loeve transformation is applied to a multi-dimensional sample data in order to diagonalize a sample covariance matrix. The null asymptotic distributions of the S2, Y2 and U2 tests are chi-squared distributions with 1, M-1 and M-2 degrees of freedom correspondingly.

`s2`	the value of the McCulloch test `S2`
`p.value.s2`	the p-value of `S2` test
`y2`	the value of the Nikulin-Rao-Robson test `Y2`
`p.value.y2`	the p-value of `Y2` test
`u2`	the value of the Dzhaparidze-Nikulin test `U2`
`p.value.u2`	the p-value of `U2` test
`data.name`	a character string giving the name of the data

The displayed result about multivariate normality is based on the McCulloch S2 test.

Vassilly Voinov, Natalya Pya, Rashid Makarov, Yevgeniy Voinov

Voinov, V., Pya, N., Makarov, R., and Voinov, Y. (2015) New invariant and consistent chi-squared type goodness-of-fit tests for multivariate normality and a related comparative simulation study. Communications in Statistics - Theory and Methods. doi link: http://www.tandfonline.com/doi/full/10.1080/03610926.2014.901370

Voinov, V., Nikulin, M. and Balakrishnan, N., Chi-squared goodness of fit tests with applications. New York: Academic Press, Elsevier, 2013

AD.test, DH.test, R.test, CM.test, HZ.test

## generating n bivariate normal random variables...       
dat <- rmvnorm(n=200,mean=rep(0,2),sigma=matrix(c(4,2,2,4),2,2)) 
res <- S2.test(dat, qqplot = FALSE)
res
## generating n bivariate t distributed with 10df random variables...       
dat <- rmvt(n=200,sigma=matrix(c(4,2,2,4),2,2)*.8,df=10,delta=rep(0,2)) 
res1 <- S2.test(dat, qqplot = TRUE)
res1

data(iris)
setosa = iris[1:50, 1:4] # Iris data only for setosa
res2 <- S2.test(setosa, qqplot = TRUE)
res2