```
library("fdaPOIFD")
# auxiliary functions to generate Gaussian processes
Cov_exponential <- function(X1, X2, alpha = NULL, beta = NULL){
x.aux <- expand.grid(i = X1, j = X2)
cov <- alpha*exp(-beta*abs(x.aux$i - x.aux$j))
Sigma <- matrix(cov, nrow = length(X1))
return(Sigma)
}
Cov_Periodic <- function(X1, X2, sigma = NULL, p = NULL, l = NULL) {
#p = period, l = wiggles, sigma = noise
Sigma <- matrix(rep(0, length(X1)*length(X2)), nrow=length(X1))
for (i in 1:nrow(Sigma)) {
for (j in 1:ncol(Sigma)) {
Sigma[i,j] <- sigma*exp(-(2*(sin(pi*abs(X1[i]-X2[j])/(p)))^2)/(l^2))
}
}
return(Sigma)
}
```

```
n <- 100
p <- 200
#parameters
time_grid <- seq(0, 1, length.out = p)
sigmaPeriodic <- Cov_Periodic(time_grid, time_grid, sigma = 3, p = 1 , l = 0.5)
sigmaExpo <- Cov_exponential(time_grid, time_grid, alpha = 0.5, beta = 5)
# Generate the random mean
centerline <- MASS::mvrnorm(1, rep(0, p), sigmaPeriodic)
# Generate the random sample
dataY <- FastGP::rcpp_rmvnorm(n, sigmaExpo, centerline)
data <- t(dataY)
colnames(data) <- as.character(c(1:n))
rownames(data) <- round(time_grid, digits=5)
dataPOFD <- intervalPOFD(data, observability = 0.5, ninterval = 4, pIncomplete = 0.75)
```

Notice that the function POIFD on fully observed data coincides with the unweighted IFD.

Install and load the Rpackage *refund*.

```
library("refund")
Fit.IV <- ccb.fpc(t(dataPOFD$pofd))
goldsmith_reconstruction <- t(Fit.IV$Yhat)
depth_goldsmith <- POIFD(goldsmith_reconstruction, type = "MBD")
```

Notice that the function POIFD on reconstructed data coincides with the unweighted IFD.

Kraus (2015) was implemented using the function *pred.missfd* obtained from the code at https://is.muni.cz/www/david.kraus/web_files/papers/partial_fda_code.zip.

Liebl (2020) was implemented using the function *reconstructKneipLiebl* obtained from the code at https://github.com/lidom/ReconstPoFD