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], na.rm=TRUE).

In R versions 3.6.0 and earlier, missing values (NA) in y typically lead to an error, whereas now the equivalent of median(*, na.rm=TRUE) is used.

Value

vector of smoothed values, the same length as y.

Author(s)

Martin Maechler

References

⁠Tukey JW (1977). Exploratory Data Analysis, number 2 series Addison-Wesley series in behavioral science. Addison-Wesley Publishing Company. ISBN 9780201076165.

⁠Velleman PF, Hoaglin DC (1981). Applications, Basics, and Computing of Exploratory Data Analysis, series Duxbury series in statistics and decision sciences. Duxbury Press. ISBN 9780878722730.

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, endrule = X)")
lines(ys, col = "light gray")
matlines(cbind(s7k, s7.,s7m), lwd = 1.5, lty = 1, col = col3)
eRules <- c("keep","constant","median")
legend("topleft", paste("endrule", eRules, sep = " = "),
       col = col3, lwd = 1.5, lty = 1, bty = "n")

stopifnot(identical(s7m, smoothEnds(s7k, 7)))

## With missing values (for R >= 3.6.1):
yN <- y; yN[c(2,40)] <- NA
rN <- sapply(eRules, function(R) runmed(yN, 7, endrule=R))
matlines(rN, type = "b", pch = 4, lwd = 3, lty=2,
         col = adjustcolor(c("red", "orange4", "orange1"), 0.5))
yN[c(1, 20:21)] <- NA # additionally
rN. <- sapply(eRules, function(R) runmed(yN, 7, endrule=R))
head(rN., 4); tail(rN.) # more NA's too, still not *so* many:
stopifnot(exprs = {
   !anyNA(rN[,2:3])
   identical(which(is.na(rN[,"keep"])), c(2L, 40L))
   identical(which(is.na(rN.), arr.ind=TRUE, useNames=FALSE),
             cbind(c(1:2,40L), 1L))
   identical(rN.[38:41, "median"], c(289,289, 397, 470))
})