robflreg (version 1.3)

rob.out.detect: Outlier detection in the functional response

Description

This function is used to detect outliers in the functional response based on a fitted function-on-function regression model in the output of rob.ff.reg.

Usage

rob.out.detect(object, alpha = 0.01, B = 200, fplot = FALSE)

Value

A vector containing the indices of outlying observations in the functional response.

Arguments

object

An output object obtained from rob.ff.reg.

alpha

Percentile of the distribution of the functional depth. The default value is 0.01.

B

The number of bootstrap samples. The default value is 200.

fplot

If TRUE, then the outlying points flagged by the method is plotted along with the values of functional response \(Y(t)\).

Author

Ufuk Beyaztas and Han Lin Shang

Details

The functional depth-based outlier detection method of Febrero-Bande et al. (2008) together with the h-modal depth proposed by Cuaves et al. (2007) is applied to the estimated residual functions obtained from rob.ff.reg to determine the outliers in the response variable. This method makes it possible to determine both magnitude and shape outliers in the response variable Hullait et al., (2021).

References

M. Febrero-Bande and P. Galeano and W. Gonzalez-Mantelga (2008), "Outlier detection in functional data by depth measures, with application to identify abnormal NOx levels", Environmetrics, 19(4), 331-345.

A. Cuaves and M. Febrero and R Fraiman (2007), "Robust estimation and classification for functional data via projection-based depth notions", Computational Statistics, 22(3), 481-496.

H. Hullait and D. S. Leslie and N. G. Pavlidis and S. King (2021), "Robust function-on-function regression", Technometrics, 63(3), 396-409.

Examples

# \donttest{
sim.data <- generate.ff.data(n.pred = 5, n.curve = 200, n.gp = 101, out.p = 0.1)
out.indx <- sim.data$out.indx
Y <- sim.data$Y
X <- sim.data$X
gpY = seq(0, 1, length.out = 101) # grid points of Y
gpX <- rep(list(seq(0, 1, length.out = 101)), 5) # grid points of Xs

model.MM <- rob.ff.reg(Y = Y, X = X, model = "full", emodel = "robust", fmodel = "MM", 
                       gpY = gpY, gpX = gpX)
rob.out.detect(object = model.MM, fplot = TRUE)
sort(out.indx)
# }