smoothVariogram: Smoothes variogram
In BiSeq: Processing and analyzing bisulfite sequencing data

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

Nonparametric smoothing with kernel regression estimators and adaptable bandwidth for variogram smoothing.

1	smoothVariogram(variogram, sill, bandwidth)

`variogram`	A `list` or a `matrix`. Usually the output of `makeVariogram`.
`sill`	A `numeric`. The sill (upper bound) of the variogram. See Details.
`bandwidth`	A numeric vector of same length as the variogram (number of rows). Default: `seq(10,1000, length.out=nrow(variogram))`. See Details.

It is necessary to smooth the variogram. Especially for greater h the variogram tends to oscillate strongly. This is the reason why the default bandwidth increases with increasing h. Nevertheless, the smoothed variogram may further increase or decrease after a horizontal part (sill). This is mostly due to the small number of observations for high distances. To wipe out this bias it is useful to set the smoothed variogram to a fixed value above a certain h, usually the mean value of the horizontal part. If a smoothed value v.sm is greater than sill for distance h_{range}, this v.sm and all other smoothed values with h > h_{range} are set to sill. Internally, the function lokerns from package lokerns is used for smoothing.

The variogram matrix (or a list with the variogram matrix) with an additional column of the smoothed v values.

Katja Hebestreit

makeVariogram, lokerns

data(vario)

# Find out the sill (this is more obvious for larger data sets):
plot(vario$variogram$v)

vario.sm <- smoothVariogram(vario, sill = 0.9)

plot(vario$variogram$v)
lines(vario.sm$variogram[,c("h", "v.sm")],
col = "red")