# smooth {stats}

### Description

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

### Usage

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

`median`

s of length **3**,

*stands for*

`3R`

**R**epeated

*until convergence, and*

`3`

*for*

`S`

**S**plitting of horizontal stretches of length 2 or 3.

Hence, * 3RS3R* is a concatenation of

`3R`

, `S`

and `3R`

, *similarly, whereas*

`3RSS`

*means first*

`3RSR`

`3R`

and then `(S and 3)`

**R**epeated until convergence -- which can be bad.

### Values

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.

### References

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

### 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.

### 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)

Documentation reproduced from R 3.0.2. License: GPL-2.