test for whether dataset comes from a known MVN

Dear all,

 

I have a multivariate dataset containing 100,000 or more points.

I want find the p-value for the dataset of points coming from a
particular multivariate normal distribution

With

mean vector u

Covariance matrix s2

So

H0: points ~ MVN( u, s2)

H1: points not ~ MVN( u, s2)

How do I find the p-value in R?

 

Googling for "Shapiro-Wilk multivariate" brings up mshapiro.test()
in the mvnormtest package.  However, I would strongly suspect that
if your data are from the real world that you will reject the null
hypothesis
of multivariate normality when you have 100,000 points -- the power
to detect tiny (unimportant?) deviations from MVN will be very high.

  cheers
    Ben Bolker

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