fda (version 6.2.0)

var.fd: Variance, Covariance, and Correlation Surfaces for Functional Data Object(s)

Description

Compute variance, covariance, and / or correlation functions for functional data.

These are two-argument functions and therefore define surfaces. If only one functional data object is supplied, its variance or correlation function is computed. If two are supplied, the covariance or correlation function between them is computed.

Usage

var.fd(fdobj1, fdobj2=fdobj1)

Value

An list object of class bifd with the following components:

coefs

the coefficient array with dimensions fdobj1[["basis"]][["nbasis"]] by fdobj2[["basis"]][["nbasis"]] giving the coefficients of the covariance matrix in terms of the bases used by fdobj1 and fdobj2.

sbasis

fdobj1[["basis"]]

tbasis

fdobj2[["basis"]]

bifdnames

dimnames list for a 4-dimensional 'coefs' array. If length(dim(coefs)) is only 2 or 3, the last 2 or 1 component of bifdnames is not used with dimnames(coefs).

Examples below illustrate this structure in simple cases.

Arguments

fdobj1, fdobj2

a functional data object.

Details

a two-argument or bivariate functional data object representing the variance, covariance or correlation surface for a single functional data object or the covariance between two functional data objects or between different variables in a multivariate functional data object.

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

mean.fd, sd.fd, std.fd stdev.fd

Examples

oldpar <- par(no.readonly=TRUE)
##
## Example with 2 different bases 
##
daybasis3 <- create.fourier.basis(c(0, 365))
daybasis5 <- create.fourier.basis(c(0, 365), 5)
tempfd3 <- with(CanadianWeather, smooth.basis(day.5, 
       dailyAv[,,"Temperature.C"], 
       daybasis3, fdnames=list("Day", "Station", "Deg C"))$fd )
precfd5 <- with(CanadianWeather, smooth.basis(day.5, 
       dailyAv[,,"log10precip"],
       daybasis5, fdnames=list("Day", "Station", "Deg C"))$fd )

# Compare with structure described above under 'value':
str(tempPrecVar3.5 <- var.fd(tempfd3, precfd5))

##
## The following produces contour and perspective plots
##

# Evaluate at a 53 by 53 grid for plotting

daybasis65 <- create.fourier.basis(rangeval=c(0, 365), nbasis=65)

daytempfd <- with(CanadianWeather, smooth.basis(day.5, 
       dailyAv[,,"Temperature.C"],
       daybasis65, fdnames=list("Day", "Station", "Deg C"))$fd )
str(tempvarbifd <- var.fd(daytempfd))

str(tempvarmat  <- eval.bifd(weeks,weeks,tempvarbifd))
# dim(tempvarmat)= c(53, 53)

par(mfrow=c(1,2), pty="s")
#contour(tempvarmat, xlab="Days", ylab="Days")
contour(weeks, weeks, tempvarmat, 
        xlab="Daily Average Temperature",
        ylab="Daily Average Temperature",
        main=paste("Variance function across locations\n",
          "for Canadian Anual Temperature Cycle"),
        cex.main=0.8, axes=FALSE)
axisIntervals(1, atTick1=seq(0, 365, length=5), atTick2=NA, 
            atLabels=seq(1/8, 1, 1/4)*365,
            labels=paste("Q", 1:4) )
axisIntervals(2, atTick1=seq(0, 365, length=5), atTick2=NA, 
            atLabels=seq(1/8, 1, 1/4)*365,
            labels=paste("Q", 1:4) )
persp(weeks, weeks, tempvarmat,
      xlab="Days", ylab="Days", zlab="Covariance")
mtext("Temperature Covariance", line=-4, outer=TRUE)
par(oldpar)