ftsa (version 6.4)

median.fts: Median functions for functional time series

Description

Computes median of functional time series at each variable.

Usage

# S3 method for fts
median(x, na.rm, method = c("hossjercroux", "coordinate", "FM", "mode", 
 "RP", "RPD", "radius"), alpha, beta, weight, ...)

Value

A list containing x = variables and y = median rates.

Arguments

x

An object of class fts.

na.rm

Remove any missing value.

method

Method for computing median.

alpha

Tuning parameter when method="radius".

beta

Trimming percentage, by default it is 0.25, when method="radius".

weight

Hard thresholding or soft thresholding.

...

Other arguments.

Author

Rob J Hyndman, Han Lin Shang

Details

If method = "coordinate", it computes a coordinate-wise median.

If method = "hossjercroux", it computes the L1-median using the Hossjer-Croux algorithm.

If method = "FM", it computes the median of trimmed functional data ordered by the functional depth of Fraiman and Muniz (2001).

If method = "mode", it computes the median of trimmed functional data ordered by \(h\)-modal functional depth.

If method = "RP", it computes the median of trimmed functional data ordered by random projection depth.

If method = "RPD", it computes the median of trimmed functional data ordered by random projection derivative depth.

If method = "radius", it computes the mean of trimmed functional data ordered by the notion of alpha-radius.

References

O. Hossjer and C. Croux (1995) "Generalized univariate signed rank statistics for testing and estimating a multivariate location parameter", Journal of Nonparametric Statistics, 4(3), 293-308.

A. Cuevas and M. Febrero and R. Fraiman (2006) "On the use of bootstrap for estimating functions with functional data", Computational Statistics and Data Analysis, 51(2), 1063-1074.

A. Cuevas 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.

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.

M. Febrero and P. Galeano and W. Gonzalez-Manteiga (2010) "Measures of influence for the functional linear model with scalar response", Journal of Multivariate Analysis, 101(2), 327-339.

J. A. Cuesta-Albertos and A. Nieto-Reyes (2010) "Functional classification and the random Tukey depth. Practical issues", Combining Soft Computing and Statistical Methods in Data Analysis, Advances in Intelligent and Soft Computing, 77, 123-130.

D. Gervini (2012) "Outlier detection and trimmed estimation in general functional spaces", Statistica Sinica, 22(4), 1639-1660.

See Also

mean.fts, var.fts, sd.fts, quantile.fts

Examples

# Calculate the median function by the different depth measures.	
median(x = ElNino_ERSST_region_1and2, method = "hossjercroux")
median(x = ElNino_ERSST_region_1and2, method = "coordinate")
median(x = ElNino_ERSST_region_1and2, method = "FM")
median(x = ElNino_ERSST_region_1and2, method = "mode")
median(x = ElNino_ERSST_region_1and2, method = "RP")
median(x = ElNino_ERSST_region_1and2, method = "RPD")
median(x = ElNino_ERSST_region_1and2, method = "radius", 
	alpha = 0.5, beta = 0.25, weight = "hard")
median(x = ElNino_ERSST_region_1and2, method = "radius", 
	alpha = 0.5, beta = 0.25, weight = "soft")