\name{tperm.fd}
\alias{tperm.fd}
\title{
  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{
  \item{x1fd}{
    a functional data object giving the first group of functional
    observations.
  }
  \item{x2fd}{
    a functional data object giving the second group of functional
    observations.
  }
  \item{nperm}{
    number of permutations to use in creating the null distribution.
  }
  \item{q}{
    Critical upper-tail quantile of the null distribution to compare to
    the observed t-statistic.
  }
  \item{argvals}{
    If \code{yfdPar} is a \code{fd} object, the points at which to
    evaluate the point-wise t-statistic.
  }
  \item{plotres}{
    Argument to plot a visual display of the null distribution
    displaying the \code{1-q}th quantile and observed t-statistic.
  }
  \item{...}{
    Additional plotting arguments that can be used with \code{plot}.
  }
}
\details{
   The usual t-statistic is calculated pointwise and the test based on
   the maximal value.  If \code{argvals} is not specified, it defaults
   to 101 equally-spaced points on the range of \code{yfdPar}.
}
\value{
  A list with the following components:

  \item{pval}{the observed p-value of the permutation test.}
  \item{qval}{the \code{q}th quantile of the null distribution.}
  \item{Tobs}{the observed maximal t-statistic.}
  \item{Tnull}{
    a vector of length \code{nperm} giving the observed values of the
    permutation distribution.
  }
  \item{Tvals}{the pointwise values of the observed t-statistic.}
  \item{Tnullvals}{
    the pointwise values of of the permutation observations.
  }
  \item{pvals.pts}{pointwise p-values of the t-statistic.}
  \item{qvals.pts}{
    pointwise \code{q}th quantiles of the null distribution
  }
  \item{argvals}{
    argument values for evaluating the F-statistic if \code{yfdPar}is
    a functional data object.
  }
}
\section{Side Effects}{
  a plot of the functional observations
}
\source{
  Ramsay, James O., and Silverman, Bernard W. (2006), \emph{Functional
    Data Analysis, 2nd ed.}, Springer, New York.
}
\seealso{
  \code{\link{fRegress}}
  \code{\link{Fstat.fd}}
%  \code{\link{tstat.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)
}
\keyword{smooth}