End Points Smoothing (for Running Medians)

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

smoothEnds(y, k = 3)

Arguments

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

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)))