Tukey's (Running Median) Smoothing

Description

Tukey's smoothers, 3RS3R, 3RSS, 3R, etc.

Usage

smooth(x, kind = c("3RS3R", "3RSS", "3RSR", "3R", "3", "S"),
       twiceit = FALSE, endrule = c("Tukey", "copy"), do.ends = FALSE)

Arguments

Details

3 is Tukey's short notation for running medians of length 3,
3R stands for Repeated 3 until convergence, and
S for Splitting of horizontal stretches of length 2 or 3.

Hence, 3RS3R is a concatenation of 3R, S and 3R, 3RSS similarly, whereas 3RSR means first 3R and then (S and 3) Repeated until convergence – which can be bad.

Value

An object of class "tukeysmooth" (which has print and summary methods) and is a vector or time series containing the smoothed values with additional attributes.

Note

S and S-PLUS use a different (somewhat better) Tukey smoother in smooth(*). Note that there are other smoothing methods which provide rather better results. These were designed for hand calculations and may be used mainly for didactical purposes.

Since R version 1.2, smooth does really implement Tukey's end-point rule correctly (see argument endrule).

kind = "3RSR" has been the default till R-1.1, but it can have very bad properties, see the examples.

Note that repeated application of smooth(*) does smooth more, for the "3RS*" kinds.

References

Tukey, J. W. (1977). Exploratory Data Analysis, Reading Massachusetts: Addison-Wesley.

See Also

runmed for running medians; lowess and loess; supsmu and smooth.spline.

Examples

require(graphics)

## see also   demo(smooth) !

x1 <- c(4, 1, 3, 6, 6, 4, 1, 6, 2, 4, 2) # very artificial
(x3R <- smooth(x1, "3R")) # 2 iterations of "3"
smooth(x3R, kind = "S")

sm.3RS <- function(x, ...)
   smooth(smooth(x, "3R", ...), "S", ...)

y <- c(1, 1, 19:1)
plot(y, main = "misbehaviour of "3RSR"", col.main = 3)
lines(sm.3RS(y))
lines(smooth(y))
lines(smooth(y, "3RSR"), col = 3, lwd = 2)  # the horror

x <- c(8:10, 10, 0, 0, 9, 9)
plot(x, main = "breakdown of  3R  and  S  and hence  3RSS")
matlines(cbind(smooth(x, "3R"), smooth(x, "S"), smooth(x, "3RSS"), smooth(x)))

presidents[is.na(presidents)] <- 0 # silly
summary(sm3 <- smooth(presidents, "3R"))
summary(sm2 <- smooth(presidents,"3RSS"))
summary(sm  <- smooth(presidents))

all.equal(c(sm2), c(smooth(smooth(sm3, "S"), "S")))  # 3RSS  === 3R S S
all.equal(c(sm),  c(smooth(smooth(sm3, "S"), "3R"))) # 3RS3R === 3R S 3R

plot(presidents, main = "smooth(presidents0, *) :  3R and default 3RS3R")
lines(sm3, col = 3, lwd = 1.5)
lines(sm, col = 2, lwd = 1.25)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(stats)
> png(filename="/home/ddbj/snapshot/RGM3/R_rel/result/stats/smooth.Rd_%03d_medium.png", width=480, height=480)
> ### Name: smooth
> ### Title: Tukey's (Running Median) Smoothing
> ### Aliases: smooth
> ### Keywords: robust smooth
> 
> ### ** Examples
> 
> require(graphics)
> 
> ## see also   demo(smooth) !
> 
> x1 <- c(4, 1, 3, 6, 6, 4, 1, 6, 2, 4, 2) # very artificial
> (x3R <- smooth(x1, "3R")) # 2 iterations of "3"
3R Tukey smoother resulting from  smooth(x = x1, kind = "3R") 
 used 2 iterations
 [1] 3 3 3 6 6 4 4 4 2 2 2
> smooth(x3R, kind = "S")
S Tukey smoother resulting from  smooth(x = x3R, kind = "S") 
 changed
 [1] 3 3 3 3 4 4 4 4 2 2 2
> 
> sm.3RS <- function(x, ...)
+    smooth(smooth(x, "3R", ...), "S", ...)
> 
> y <- c(1, 1, 19:1)
> plot(y, main = "misbehaviour of "3RSR"", col.main = 3)
> lines(sm.3RS(y))
> lines(smooth(y))
> lines(smooth(y, "3RSR"), col = 3, lwd = 2)  # the horror
> 
> x <- c(8:10, 10, 0, 0, 9, 9)
> plot(x, main = "breakdown of  3R  and  S  and hence  3RSS")
> matlines(cbind(smooth(x, "3R"), smooth(x, "S"), smooth(x, "3RSS"), smooth(x)))
> 
> presidents[is.na(presidents)] <- 0 # silly
> summary(sm3 <- smooth(presidents, "3R"))
3R Tukey smoother resulting from
 smooth(x = presidents, kind = "3R") ;  n = 120 
 used 4 iterations
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    0.0    44.0    57.0    54.2    71.0    82.0 
> summary(sm2 <- smooth(presidents,"3RSS"))
3RSS Tukey smoother resulting from
 smooth(x = presidents, kind = "3RSS") ;  n = 120 
 used 5 iterations
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   0.00   44.00   57.00   55.45   69.00   82.00 
> summary(sm  <- smooth(presidents))
3RS3R Tukey smoother resulting from
 smooth(x = presidents) ;  n = 120 
 used 7 iterations
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  24.00   44.00   57.00   55.88   69.00   82.00 
> 
> all.equal(c(sm2), c(smooth(smooth(sm3, "S"), "S")))  # 3RSS  === 3R S S
[1] TRUE
> all.equal(c(sm),  c(smooth(smooth(sm3, "S"), "3R"))) # 3RS3R === 3R S 3R
[1] TRUE
> 
> plot(presidents, main = "smooth(presidents0, *) :  3R and default 3RS3R")
> lines(sm3, col = 3, lwd = 1.5)
> lines(sm, col = 2, lwd = 1.25)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>