# smoothEnds

##### End Points Smoothing (for Running Medians)

Smooth end points of a vector `y`

using subsequently smaller
medians and Tukey's end point rule at the very end. (of odd span),

##### Usage

`smoothEnds(y, k = 3)`

##### Arguments

- y
dependent variable to be smoothed (vector).

- k
width of largest median window; must be odd.

##### Details

`smoothEnds`

is used to only do the ‘end point smoothing’,
i.e., change at most the observations closer to the beginning/end
than half the window `k`

. The first and last value are computed using
*Tukey's end point rule*, i.e.,
`sm[1] = median(y[1], sm[2], 3*sm[2] - 2*sm[3])`

.

##### Value

vector of smoothed values, the same length as `y`

.

##### References

John W. Tukey (1977)
*Exploratory Data Analysis*, Addison.

Velleman, P.F., and Hoaglin, D.C. (1981)
*ABC of EDA (Applications, Basics, and Computing of Exploratory
Data Analysis)*; Duxbury.

##### See Also

`runmed(*, endrule = "median")`

which calls
`smoothEnds()`

.

##### Examples

`library(stats)`

```
# NOT RUN {
require(graphics)
y <- ys <- (-20:20)^2
y [c(1,10,21,41)] <- c(100, 30, 400, 470)
s7k <- runmed(y, 7, endrule = "keep")
s7. <- runmed(y, 7, endrule = "const")
s7m <- runmed(y, 7)
col3 <- c("midnightblue","blue","steelblue")
plot(y, main = "Running Medians -- runmed(*, k=7, end.rule = X)")
lines(ys, col = "light gray")
matlines(cbind(s7k, s7.,s7m), lwd = 1.5, lty = 1, col = col3)
legend(1, 470, paste("endrule", c("keep","constant","median"), sep = " = "),
col = col3, lwd = 1.5, lty = 1)
stopifnot(identical(s7m, smoothEnds(s7k, 7)))
# }
```

*Documentation reproduced from package stats, version 3.6.0, License: Part of R 3.6.0*