fda (version 2.4.0)

tperm.fd: 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.

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

source

Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

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.

See Also

fRegress Fstat.fd

Examples

# 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(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)