smooth {stats} R Documentation

## 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

 x a vector or time series kind a character string indicating the kind of smoother required; defaults to "3RS3R". twiceit logical, indicating if the result should be ‘twiced’. Twicing a smoother S(y) means S(y) + S(y - S(y)), i.e., adding smoothed residuals to the smoothed values. This decreases bias (increasing variance). endrule a character string indicating the rule for smoothing at the boundary. Either "Tukey" (default) or "copy". do.ends logical, indicating if the 3-splitting of ties should also happen at the boundaries (ends). This is only used for kind = "S".

### 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.

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

### Examples

require(graphics)

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"))