fRegress.stderr: Compute Standard errors of Coefficient Functions Estimated by...

In fda: Functional Data Analysis

Compute Standard errors of Coefficient Functions Estimated by Functional Regression Analysis

Description

Function 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 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

## S3 method for class 'stderr'
fRegress(y, y2cMap, SigmaE, returnMatrix=FALSE, ...)

Arguments

y	the named list that is returned from a call to function fRegress, where it is referred to as fRegressList. (R syntax requires that the first argument of any function beginning with fRegress. must begin with y.)
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 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.
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.
returnMatrix	logical: If TRUE, a two-dimensional is returned using a special class from the Matrix package.
...	optional arguments not used by fRegress.stderr but needed for superficial compatibility with fRegress methods.

Value

a named list of length 3 containing:

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.
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.
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), 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, fRegress.CV

Examples

#See the weather data analyses in the file daily.ssc for
#examples of the use of function fRegress.stderr.

fda documentation built on Sept. 30, 2024, 9:19 a.m.