fRegress.stderr.Rd

\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{
\method{fRegress}{stderr}(y, y2cMap, SigmaE, returnMatrix=FALSE, ...)
}
\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{returnMatrix}{
    logical:  If TRUE,  a two-dimensional is returned using a
    special class from the Matrix package.
  }
  \item{\dots}{
    optional arguments not used by \code{fRegress.stderr} but needed for
    superficial compatibility 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.}
}
\references{
  Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009),
    \emph{Functional data analysis with R and Matlab}, Springer, New York.
  
  Ramsay, James O., and Silverman, Bernard W. (2005), 
    \emph{Functional Data Analysis, 2nd ed.}, Springer, New York.
  
  Ramsay, James O., and Silverman, Bernard W. (2002), 
    \emph{Applied Functional Data Analysis}, Springer, New York.
}
\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}