stats (version 3.3)

runmed: Running Medians -- Robust Scatter Plot Smoothing

Description

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.

Usage

runmed(x, k, endrule = c("median", "keep", "constant"),
       algorithm = NULL, print.level = 0)

Arguments

x

numeric vector, the dependent variable to be smoothed.

k

integer width of median window; must be odd. Turlach had a default of k <- 1 + 2 * min((n-1)%/% 2, ceiling(0.1*n)). Use k = 3 for minimal robust smoothing eliminating isolated outliers.

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: [object Object],[object Object],[object Object]

algorithm

character string (partially matching "Turlach" or "Stuetzle") or the default NULL, specifying which algorithm should be applied. The default choice depends on n = length(x) and k where "Turlach" will be used for larger problems.

print.level

integer, indicating verboseness of algorithm; should rarely be changed by average users.

Value

• vector of smoothed values of the same length as x with an attribute k containing (the oddified) k.

encoding

UTF-8

Details

Apart from the end values, the result y = runmed(x, k) simply has y[j] = median(x[(j-k2):(j+k2)]) (k = 2*k2+1), computed very efficiently.

The two algorithms are internally entirely different: [object Object],[object Object]

Currently long vectors are only supported for algorithm = "Steutzle".

References

Härdle{Haerdle}, 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.

See Also

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.

Examples

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)) # 1-neighbourhood <==> 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))