| 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 |
twiceit |
logical, indicating if the result should be ‘twiced’.
Twicing a smoother |
endrule |
a character string indicating the rule for smoothing at the
boundary. Either |
do.ends |
logical, indicating if the 3-splitting of ties should
also happen at the boundaries (ends). This is only used for
|
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
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" had 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)