R: Functional outlier detection methods.

foutliers {rainbow} | R Documentation

## 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, method = "depth.trim")

[Package rainbow version 3.5 Index]