R: Fréchet Variance Trajectory for densities

VarObj {frechet}

R Documentation

Fréchet Variance Trajectory for densities

Description

Modeling time varying density objects with respect to $L^2$-Wasserstein distance by Fréchet variance trajectory

Usage

VarObj(tgrid, yin = NULL, hin = NULL, din = NULL, qin = NULL, optns = list())

Arguments

`tgrid`	Time grid vector for the time varying object data.
`yin`	An array or list of lists holding the samples of observations. If `yin` is an array, it has size `n` x `length(tgrid)` x numbers of samples holding the observation, such that `yin[i,j,]` holds the observations to the ith sample at the jth time grid. If `yin` is a list of lists, `yin[[i]][[j]]` holds the observations to the ith sample at the jth time grid.
`hin`	A list of lists holding the histogram for each subject. `hin[[i]][[j]]` holds the histogram to the ith sample at the jth time grid.
`din`	A three dimension array of size `n` x `length(tgrid)` x `length(optns$dSup)` holding the observed densities, such that `din[i,j,]` holds the observed density function taking values on `optns$dSup` corresponding to the ith sample at the jth time grid.
`qin`	A three dimension array of size `n` x `length(tgrid)` x `length(optns$qSup)` holding the observed quantiles, such that `din[i,j,]` holds the observed density function taking values on `optns$qSup` corresponding to the ith sample at the jth time grid. Note that only one of `yin`, `hin`, `din` and `qin` needs to be input. If more than one of them are specified, `yin` overwrites `hin`, `hin` overwrites `din` and `din` overwrites `qin`. where each row holds the observations for one subject on the common grid `tGrid`.
`optns`	a list of options control parameters specified by `list(name=value)`.

Details

Available control options are qSup, nqSup, dSup and other options in FPCA of fdapace.

Value

A list of the following:

`tgridout`	Time grid vector for the output time varying object data.
`K`	Numbers of principal components.
`nu`	A vector of dimension `length(tgridout)` giving the mean function support on `tgridout` of the Fréchet variance function.
`lambda`	A vector of dimension `K` containing eigenvalues.
`phi`	A `length(tgridout)` X `K` matrix containing eigenfunctions support on `tgridout` of the Fréchet variance function.
`xiEst`	A `n` X `K` matrix containing the FPC estimates.
`cumFVE`	A vector of dimension `K` with the fraction of the cumulative total variance explained with each additional FPC.
`FPCAObj`	FPCA Object of Fréchet variance function.
`tgridin`	Input `tgrid`.
`qSup`	A vector of dimension `length(tgridin)` giving the domain grid of quantile functions `qout`.
`qout`	A three dimension array of dimension `n` x `length(tgridin)` x `length(qSup)` holding the observed quantiles, such that `qout[i,j,]` holds the observed density function taking values on `qSup` corresponding to the ith sample at the jth time grid.
`qmean`	A `length(tgridin)` X `length(qSup)` matrix containing the time varying Fréchet mean function.
`VarTraj`	A `n` X `length(tgridin)` matrix containing the variance trajectory.

References

Dubey, P., & Müller, H. G. (2021). Modeling Time-Varying Random Objects and Dynamic Networks. Journal of the American Statistical Association, 1-33.

Examples


set.seed(1)
#use yin 
tgrid = seq(1, 50, length.out = 50)
dSup = seq(-10, 60, length.out = 100)
yin = array(dim=c(30, 50, 100))
for(i in 1:30){
  yin[i,,] = t(sapply(tgrid, function(t){
    rnorm(100, mean = rnorm(1, mean = 1, sd = 1/t))
  }))
}
result1 = VarObj(tgrid, yin = yin)
plot(result1$phi[,1])
plot(result1$phi[,2])
yin2 = replicate(30, vector("list", 50), simplify = FALSE)
for(i in 1:30){
  for(j in 1:50){
    yin2[[i]][[j]] = yin[i,j,]
  }}
result1 = VarObj(tgrid, yin = yin2)

# use hin
tgrid = seq(1, 50, length.out = 50)
dSup = seq(-10, 60, length.out = 100)
hin =  replicate(30, vector("list", 50), simplify = FALSE)
for(i in 1:30){
  for (j in 1:50){
    hin[[i]][[j]] = hist(yin[i,j,])
  }
}
result2 = VarObj(tgrid, hin = hin)

# use din
tgrid = seq(1, 50, length.out = 50)
dSup = seq(-10, 60, length.out = 100)
din = array(dim=c(30, 50, 100))
for(i in 1:30){
  din[i,,] = t(sapply(tgrid, function(t){
    dnorm(dSup, mean = rnorm(1, mean = t, sd = 1/t))
  }))
}
result3 = VarObj(tgrid, din = din, optns=list(dSup = dSup))

# use qin
tgrid = seq(1, 50, length.out = 50)
qSup = seq(0.00001,1-0.00001,length.out = 100)
qin = array(dim=c(30, 50, 100))
for(i in 1:30){
  qin[i,,] = t(sapply(tgrid, function(t){
    qnorm(qSup, mean = rnorm(1, mean = t, sd = 1/t))
  }))
}
result4 = VarObj(tgrid, qin = qin, optns=list(qSup = round(qSup, 4)))

[Package frechet version 0.3.0 Index]