Standard deviation functions for functional time series
Computes standard deviation of functional time series at each variable.
## S3 method for class 'fts'
sd(x, method = c("coordinate", "FM", "mode", "RP", "RPD", "radius"),
trim = 0.25, alpha, weight,...)x |
An object of class |
method |
Method for computing median. |
trim |
Percentage of trimming. |
alpha |
Tuning parameter when |
weight |
Hard thresholding or soft thresholding. |
... |
Other arguments. |
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.
A list containing x = variables and y = standard deviation rates.
Han Lin Shang
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.
# 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")
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