foutliers {rainbow}

Functional outlier detection methods.

Description

Functional outlier detection methods.

Usage

foutliers(data, method = c("robMah", "lrt", "depth.trim", "depth.pond", 
 "HUoutliers"), dfunc = depth.mode, nb = 200, suav = 0.05, trim = 0.1, 
  order = 2, lambda = 3.29,...)

Arguments

data

An object of class fds or fts.

method

Outlier detection method.

dfunc

When method = "lrt" or method = "depth.trim" or method = "depth.pond", users can specify the type of depth functions with possible choices of depth.FM, depth.mode, depth.RP, depth.RPD.

nb

When method = "lrt", users can specify the number of bootstrap samples.

suav

When method = "lrt", users can specify the smoothing parameter used in the smoothed bootstrap samples to determine the cutoff value.

trim

When method = "lrt" or method = "depth.trim" or method = "depth.pond", users can specify the trimming percentage.

order

When method = "HUoutliers", users can specify the number of principal components.

lambda

When method = "HUoutliers", users can specify the value of tuning parameter.

...

Other arguments.

Details

When method = "lrt", the outlier detection method corresponds to the approach of Febrero et al. (2007) using the likelihood ratio test.

When method = "depth.trim", the outlier detection method corresponds to the approach of Febrero et al. (2008) using the functional depth with trimmed curves.

When method = "depth.pond", the outlier detection method corresponds to the approach of Febrero et al. (2008) using the functional depth with all curves.

When method = "HUoutliers", the outlier detection method corresponds to the approach of Hyndman and Ullah (2008) using the integrated square forecast errors.

When method = "robMah", the outlier detection method corresponds to the approach of Rousseeuw and Leroy (1987) using the robust Mahalanobis distance.

Value

A list containing the following components is returned.

outliers

Detected outliers.

cutoff

Threshold value to separate outliers from non-outliers, when method = "lrt", method = "depth.trim", and method = "depth.pond".

depth.total

Depth measure of each functional curve.

depth.out

Depth measure of functional outliers.

Author(s)

Han Lin Shang

References

P. Rousseeuw and A. Leroy (1987) Robust regression and outlier detection, John Wiley and Sons, New York.

A. Atkinson (1994) "Fast very robust methods for the detection of multiple outliers", Journal of the American Statistical Association, 89(428), 1329-1339.

R. J. Hyndman and M. S. Ullah (2007) "Robust forecasting of mortality and fertility rates: A functional data approach", Computational Statistics and Data Analysis, 51(10), 4942-4956.

M. Febrero and P. Galeano and W. Gonzalez-Manteiga (2007) "A functional analysis of NOx levels: location and scale estimation and outlier detection", Computational Statistics, 22(3), 411-427.

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

R. J. Hyndman and H. L. Shang. (2010) "Rainbow plots, bagplots, and boxplots for functional data", Journal of Computational and Graphical Statistics, 19(1), 29-45.

Examples

foutliers(data = ElNino_OISST_region_1and2, method = "depth.trim")