funData (version 1.3-9)

addError: Add Gaussian white noise to functional data objects

Description

This function generates an artificial noisy version of a functional data object of class funData (univariate) or multiFunData (multivariate) by adding iid. realizations of Gaussian random variables \(\varepsilon \sim \mathcal{N}(0, \sigma^2)\) to the observations. The standard deviation \(\sigma\) can be supplied by the user.

Usage

addError(funDataObject, sd)

Value

An object of the same class as funDataObject, which is a noisy version of the original data.

Arguments

funDataObject

A functional data object of class funData or multiFunData.

sd

The standard deviation \(\sigma\) of the Gaussian white noise that is added to the data. Defaults to 1. See Description.

See Also

funData, multiFunData, simFunData, simMultiFunData.

Examples

oldPar <- par(no.readonly = TRUE)
set.seed(1)

# Univariate functional data
plain <- simFunData(argvals = seq(0,1,0.01), M = 10, eFunType = "Fourier",
                    eValType = "linear", N = 1)$simData
noisy <- addError(plain , sd = 0.5)
veryNoisy <- addError(plain, sd = 2)

plot(plain, main = "Add error", ylim = range(veryNoisy@X))
plot(noisy, type = "p", pch = 20, add = TRUE)
plot(veryNoisy, type = "p", pch = 4, add = TRUE)
legend("topright", c("Plain", "Noisy", "Very Noisy"), lty = c(1, NA, NA), pch = c(NA, 20 ,4))

# Multivariate functional data
plain <- simMultiFunData(type = "split", argvals = list(seq(0,1,0.01), seq(-.5,.5,0.02)), M = 10,
                        eFunType = "Fourier", eValType = "linear", N = 1)$simData
noisy <- addError(plain , sd = 0.5)
veryNoisy <- addError(plain, sd = 2)

par(mfrow = c(1,2))
plot(plain[[1]], main = "Add error (multivariate)", ylim = range(veryNoisy[[1]]@X))
plot(noisy[[1]], type = "p", pch = 20, add = TRUE)
plot(veryNoisy[[1]], type = "p", pch = 4, add = TRUE)

plot(plain[[2]], main = "Add error (multivariate)", ylim = range(veryNoisy[[2]]@X))
plot(noisy[[2]], type = "p", pch = 20, add = TRUE)
plot(veryNoisy[[2]], type = "p", pch = 4, add = TRUE)
legend("topright", c("Plain", "Noisy", "Very Noisy"), lty = c(1, NA, NA), pch = c(NA, 20 ,4))

par(oldPar)