\name{fRegress.stderr}
\alias{fRegress.stderr}
\title{
Compute Standard errors of Coefficient Functions Estimated by
Functional Regression Analysis
}
\description{
Function \code{fRegress} carries out a functional regression analysis
of the concurrent kind, and estimates a regression coefficient
function corresponding to each independent variable, whether it is
scalar or functional. This function uses the list that is output by
\code{fRegress} to provide standard error functions for each
regression function. These standard error functions are pointwise,
meaning that sampling standard deviation functions only are computed,
and not sampling covariances.
}
\usage{
fRegress.stderr(y, y2cMap, SigmaE, ...)
}
\arguments{
\item{y}{
the named list that is returned from a call to
function \code{fRegress}, where it is referred to as fRegressList.
R syntax requires that the first argument of any function beginning
with \code{fRegress.} must begin with \code{y}.
}
\item{y2cMap}{
a matrix that contains the linear transformation that takes the raw
data values into the coefficients defining a smooth functional data
object. Typically, this matrix is returned from a call to function
\code{smooth.basis} that generates the dependent variable objects.
If the dependent variable is scalar, this matrix is an identity
matrix of order equal to the length of the vector.
}
\item{SigmaE}{
either a matrix or a bivariate functional data object according to
whether the dependent variable is scalar or functional,
respectively. This object has a number of replications equal to the
length of the dependent variable object. It contains an estimate of
the variance-covariance matrix or function for the residuals.
}
\item{\dots}{
optional arguments not used by \code{fRegress.stderr} but needed for
superficial compatibability with \code{fRegress} methods.
}
}
\value{
a named list of length 3 containing:
\item{betastderrlist}{
a list object of length the number of independent variables. Each
member contains a functional parameter object for the standard error
of a regression function.
}
\item{bvar}{
a symmetric matrix containing sampling variances and covariances for
the matrix of regression coefficients for the regression functions.
These are stored column-wise in defining BVARIANCE.
}
\item{c2bMap}{
a matrix containing the mapping from response variable coefficients to
coefficients for regression coefficients.
}
}
\seealso{
\code{\link{fRegress}},
\code{\link{fRegress.CV}}
}
\examples{
#See the weather data analyses in the file daily.ssc for
#examples of the use of function fRegress.stderr.
}
% docclass is function
\keyword{smooth}