smoothEnds: End Points Smoothing (for Running Medians)

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

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

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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.

Author(s)

Martin Maechler

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

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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)))