ftsa (version 5.5)

sd.fts: Standard deviation functions for functional time series

Description

Computes standard deviation of functional time series at each variable.

Usage

# S3 method for fts
sd(x, method = c("coordinate", "FM", "mode", "RP", "RPD", "radius"), 
 trim = 0.25, alpha, weight,...)

Arguments

x

An object of class fts.

method

Method for computing median.

trim

Percentage of trimming.

alpha

Tuning parameter when method="radius".

weight

Hard thresholding or soft thresholding.

...

Other arguments.

Value

A list containing x = variables and y = standard deviation rates.

Details

If method = "coordinate", it computes coordinate-wise standard deviation functions.

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

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

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

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

If method = "radius", it computes the standard deviation function 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", 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 \& 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, median.fts, var.fts, quantile.fts

Examples

# NOT RUN {
# Fraiman-Muniz depth was arguably the oldest functional depth.	
sd(x = ElNino_ERSST_region_1and2, method = "FM")
sd(x = ElNino_ERSST_region_1and2, method = "coordinate")
sd(x = ElNino_ERSST_region_1and2, method = "mode")
sd(x = ElNino_ERSST_region_1and2, method = "RP")
sd(x = ElNino_ERSST_region_1and2, method = "RPD")
sd(x = ElNino_ERSST_region_1and2, method = "radius", 
	alpha = 0.5, weight = "hard")
sd(x = ElNino_ERSST_region_1and2, method = "radius", 
	alpha = 0.5, weight = "soft")
# }