Compute running medians of odd span. This is the ‘most robust’ scatter plot smoothing possible. For efficiency (and historical reason), you can use one of two different algorithms giving identical results.
1 2 
x 
numeric vector, the ‘dependent’ variable to be smoothed. 
k 
integer width of median window; must be odd. Turlach had a
default of 
endrule 
character string indicating how the values at the beginning and the end (of the data) should be treated. Can be abbreviated. Possible values are:

algorithm 
character string (partially matching 
print.level 
integer, indicating verboseness of algorithm; should rarely be changed by average users. 
Apart from the end values, the result y = runmed(x, k)
simply has
y[j] = median(x[(jk2):(j+k2)])
(k = 2*k2+1
), computed very
efficiently.
The two algorithms are internally entirely different:
"Turlach"
is the Härdle–Steiger
algorithm (see Ref.) as implemented by Berwin Turlach.
A tree algorithm is used, ensuring performance O(n * log(k)) where n = length(x)
which is
asymptotically optimal.
"Stuetzle"
is the (older) Stuetzle–Friedman implementation which makes use of median updating when one observation enters and one leaves the smoothing window. While this performs as O(n * k) which is slower asymptotically, it is considerably faster for small k or n.
Currently long vectors are only supported for algorithm = "Steutzle"
.
vector of smoothed values of the same length as x
with an
attr
ibute k
containing (the ‘oddified’)
k
.
Martin Maechler [email protected], based on Fortran code from Werner Stuetzle and SPLUS and C code from Berwin Turlach.
Härdle, W. and Steiger, W. (1995) [Algorithm AS 296] Optimal median smoothing, Applied Statistics 44, 258–264.
Jerome H. Friedman and Werner Stuetzle (1982) Smoothing of Scatterplots; Report, Dep. Statistics, Stanford U., Project Orion 003.
Martin Maechler (2003) Fast Running Medians: Finite Sample and Asymptotic Optimality; working paper available from the author.
smoothEnds
which implements Tukey's end point rule and
is called by default from runmed(*, endrule = "median")
.
smooth
uses running
medians of 3 for its compound smoothers.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33  require(graphics)
utils::example(nhtemp)
myNHT < as.vector(nhtemp)
myNHT[20] < 2 * nhtemp[20]
plot(myNHT, type = "b", ylim = c(48, 60), main = "Running Medians Example")
lines(runmed(myNHT, 7), col = "red")
## special: multiple y values for one x
plot(cars, main = "'cars' data and runmed(dist, 3)")
lines(cars, col = "light gray", type = "c")
with(cars, lines(speed, runmed(dist, k = 3), col = 2))
## nice quadratic with a few outliers
y < ys < (20:20)^2
y [c(1,10,21,41)] < c(150, 30, 400, 450)
all(y == runmed(y, 1)) # 1neighbourhood <==> interpolation
plot(y) ## lines(y, lwd = .1, col = "light gray")
lines(lowess(seq(y), y, f = 0.3), col = "brown")
lines(runmed(y, 7), lwd = 2, col = "blue")
lines(runmed(y, 11), lwd = 2, col = "red")
## Lowess is not robust
y < ys ; y[21] < 6666 ; x < seq(y)
col < c("black", "brown","blue")
plot(y, col = col[1])
lines(lowess(x, y, f = 0.3), col = col[2])
lines(runmed(y, 7), lwd = 2, col = col[3])
legend(length(y),max(y), c("data", "lowess(y, f = 0.3)", "runmed(y, 7)"),
xjust = 1, col = col, lty = c(0, 1, 1), pch = c(1,NA,NA))

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