Mean functions for functional time series

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Description

Computes mean of functional time series at each variable.

Usage

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

Arguments

x

An object of class fts.

method

Method for computing the mean function.

na.rm

A logical value indicating whether NA values should be stripped before the computation proceeds.

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.

Details

If method = "coordinate", it computes the coordinate-wise functional mean.

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

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

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

If method = "RPD", it computes the mean 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.

Value

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

Author(s)

Rob J Hyndman, Han Lin Shang

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 \& 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, Volume 77, 123-130.

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

See Also

median.fts, var.fts, sd.fts, quantile.fts

Examples

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

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