| smooth {stats} | R Documentation |
Tukey's smoothers, 3RS3R, 3RSS, 3R, etc.
smooth(x, kind = c("3RS3R", "3RSS", "3RSR", "3R", "3", "S"),
twiceit = FALSE, endrule = "Tukey", do.ends = FALSE)
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 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 |
do.ends |
logical, indicating if the 3-splitting of ties should
also happen at the boundaries (ends). This is only used for
|
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.
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.
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.
Tukey, J. W. (1977). Exploratory Data Analysis, Reading Massachusetts: Addison-Wesley.
lowess;
loess,
supsmu and
smooth.spline.
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)