mrct.ise {mrct}

Integrated square error

Description

Calculates the approximation of the integrated square error between the estimated covariance based on non-outlying curves of a data set determined by the MRCT estimator and the true kernel for one of the three outlier settings in the simulation study of Oguamalam et al. 2023.

Usage

mrct.ise(data, outliers.est, model)

Arguments

data

Numeric matrix of a functional data set for which the esimator has to be calculated. Each row contains an observation. They are assumed to be observed on the same regular grid.

outliers.est

Integer vector containing the indices of outliers.

model

Integer. 1 correspond to the first outlier setting, whereas 2 and 3 are related to the remaining two, which both have the same kernel.

Value

Numeric value containing the approximated integrated square error between estimated and theoretical covariance.

References

Oguamalam J, Radojičić U, Filzmoser P (2023). “Minimum regularized covariance trace estimator and outlier detection for functional data.” https://doi.org/10.48550/arXiv.2307.13509..

Examples

# Fix seed for reproducibility
set.seed(124)

# Sample outlying indices
cont.ind <- sample(1:100,size=10)

# Generate 100 curves on the interval [0,1] at 150 timepoints with 20% outliers.
y <- mrct.rgauss(x.grid=seq(0,1,length.out=150), N=100, model=1,
                 outliers=cont.ind, method="linear")
# Run MRCT
mrct.y <- mrct(data=y, h=0.75, alpha=0.1,
               initializations=10, criterion="sum")
# Two additional curves are regarded as outlying according to the algorithm
mrct.y$theoretical.w %in% cont.ind
# Compare the ISE between true kernel and 1) true non-outliers,
# 2) estimated non-outliers and 3) the complete data
ise1 <- mrct.ise(data=y, outliers.est=cont.ind, model=1)
ise2 <- mrct.ise(data=y, outliers.est=mrct.y$theoretical.w, model=1)
ise3 <- mrct.ise(data=y, outliers.est=c(), model=1)
ise1; ise2; ise3