tperm.fd {fda}

Permutation t-test for two groups of functional data objects.

Description

tperm.fd creates a null distribution for a test of no difference between two groups of functional data objects.

Usage

tperm.fd(x1fd, x2fd, nperm=200, q=0.05, argvals=NULL, plotres=TRUE, ...)

Arguments

x1fd

a functional data object giving the first group of functional observations.

x2fd

a functional data object giving the second group of functional observations.

nperm

number of permutations to use in creating the null distribution.

q

Critical upper-tail quantile of the null distribution to compare to the observed t-statistic.

argvals

If yfdPar is a fd object, the points at which to evaluate the point-wise t-statistic.

plotres

Argument to plot a visual display of the null distribution displaying the 1-qth quantile and observed t-statistic.

...

Additional plotting arguments that can be used with plot.

Details

The usual t-statistic is calculated pointwise and the test based on the maximal value. If argvals is not specified, it defaults to 101 equally-spaced points on the range of yfdPar.

Value

A list with the following components:

pval

the observed p-value of the permutation test.

qval

the qth quantile of the null distribution.

Tobs

the observed maximal t-statistic.

Tnull

a vector of length nperm giving the observed values of the permutation distribution.

Tvals

the pointwise values of the observed t-statistic.

Tnullvals

the pointwise values of of the permutation observations.

pvals.pts

pointwise p-values of the t-statistic.

qvals.pts

pointwise qth quantiles of the null distribution

argvals

argument values for evaluating the F-statistic if yfdParis a functional data object.

Side Effects

a plot of the functional observations

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

fRegress Fstat.fd

Examples

oldpar <- par(no.readonly=TRUE)
# This tests the difference between boys and girls heights in the
# Berkeley growth data.

# First set up a basis system to hold the smooths

knots    <- growth$age
norder   <- 6
nbasis   <- length(knots) + norder - 2
hgtbasis <- create.bspline.basis(range(knots), nbasis, norder, knots)

# Now smooth with a fourth-derivative penalty and a very small smoothing
# parameter

Lfdobj <- 4
lambda <- 1e-2
growfdPar <- fdPar(fd(matrix(0,nbasis,1), hgtbasis), Lfdobj, lambda)

hgtmfd <- smooth.basis(growth$age, growth$hgtm, growfdPar)$fd
hgtffd <- smooth.basis(growth$age, growth$hgtf, growfdPar)$fd

# Call tperm.fd

tres <- tperm.fd(hgtmfd,hgtffd)
par(oldpar)