tests function

Formal Tests of Multivariate Normality

Compute formal tests based on the Mahalanobis distances and Mahalanobis angles of multivariate normality (including Mardia's kurtosis test and Mardia's skewness test).

maha2_test(x, type = c("ad.test", "ks.test"), dist = c("chi2", "beta"), ...)
mardia_test(x, type = c("kurtosis", "skewness"), method = c("direct", "chol"))

Arguments

• x: (n, d)-matrix of data.

• type: character string indicating the type of test:

  • "ad.test":: Anderson-Darling test as computed by the underlying ad.test().
  • "ks.test":: Kolmogorov-Smirnov test as computed by the underlying ks.test().
  • "kurtosis":: Mardia's kurtosis test (based on Mahalanobis distances).
  • "skewness":: Mardia's skewness test (based on Mahalanobis angles).

• dist: distribution to check against.

• method: method for computing the Mahalanobis angles.

• ...: additional arguments passed to the underlying ad.test() or ks.test().

Returns

An htest object (for maha2_test the one returned by the underlying ad.test() or ks.test()).

Author(s)

Marius Hofert

Examples

set.seed(271)
U <- matrix(runif(3 * 200), ncol = 3)
X <- cbind(qexp(U[,1]), qnorm(U[,2:3]))
maha2_test(X) # at the 'edge' of rejecting
maha2_test(X, type = "ks.test") # at the 'edge', too
mardia_test(X) # clearly rejects at 5%
mardia_test(X, type = "skewness") # clearly rejects at 5%