qmvt.sim(vmat, lmat, error.df=Inf, simsize=12999, alpha=.05, two.sided=T)
vmat
(if any).
Inf
is accepted.
simsize
should be chosen to be on the order of at least the default size.
1-alpha
quantile for the
distribution of the maximum of multivariate-t random variables.
TRUE
, the default,
the quantile is for the distribution of the maximum absolute value of
the multivariate-t random variables.
Otherwise, the absolute value is not taken.
1-alpha
) quantile of the distribution
of the pivotal quantity specified below.
Suppose Z = (Z1, Z2, ... Zk) are multivariate normal variables with
means 0 and covariance matrix
vmat
.
Let U be a random variable independent of Z,
such that df*U^2 is Chisquare with df degrees of freedom.
Suppose
lmat
has p columns.
If
two.sided
is
TRUE
, the pivotal quantity for
qmvt.sim
is defined to be
D = max{1<=j<=p: | lmat[,j]*Z | / U}.
If
two.sided
is
FALSE
, the pivotal quantity is the above without
absolute values.
The function approximates the
1-alpha
quantile by simulating the
pivotal quantity the specified number of times
and selecting the
(1-alpha)*(simsize+1)
smallest value
from the simulated versions.
Of course, the actual value of the critical point generated
will vary between simulations.
Repeated generations of critical points in an attempt to obtain smaller values
renders this method invalid.
Edwards, D. and Berry, J. J. (1987). The efficiency of simulation-based multiple comparisons. Biometrics 43, 913-928.
# compare to qmvt(.90, 20, 60, .10) qmvt.sim(diag(20), diag(20), 60, alpha=.10)