varDiff: Estimation of scale based on sequential-order differences

Description

Estimation of scale based on sequential-order differences, corresponding to the scale estimates provided by var, sd, mad and IQR.

Usage

varDiff(x, idxs = NULL, na.rm = FALSE, diff = 1L, trim = 0, ...)
sdDiff(x, idxs = NULL, na.rm = FALSE, diff = 1L, trim = 0, ...)
madDiff(x, idxs = NULL, na.rm = FALSE, diff = 1L, trim = 0,
  constant = 1.4826, ...)
iqrDiff(x, idxs = NULL, na.rm = FALSE, diff = 1L, trim = 0, ...)
rowVarDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ...)
colVarDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ...)
rowSdDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ...)
colSdDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ...)
rowMadDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ...)
colMadDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ...)
rowIQRDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ...)
colIQRDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ...)

Arguments

A numeric vector of length N or a numeric NxK matrix.

idxs, rows, cols

A vector indicating subset of elements (or rows and/or columns) to operate over. If NULL, no subsetting is done.

na.rm

If TRUE, NAs are excluded, otherwise not.

diff

The positional distance of elements for which the difference should be calculated.

trim

A double in [0,1/2] specifying the fraction of observations to be trimmed from each end of (sorted) x before estimation.

...

Not used.

constant

A scale factor adjusting for asymptotically normal consistency.

Value

Returns a numeric vector of length 1, length N, or length K.

Details

Note that n-order difference MAD estimates, just like the ordinary MAD estimate by mad, apply a correction factor such that the estimates are consistent with the standard deviation under Gaussian distributions.

The interquartile range (IQR) estimates does not apply such a correction factor. If asymptotically normal consistency is wanted, the correction factor for IQR estimate is 1 / (2 * qnorm(3/4)), which is half of that used for MAD estimates, which is 1 / qnorm(3/4). This correction factor needs to be applied manually, i.e. there is no constant argument for the IQR functions.

References

[1] J. von Neumann et al., The mean square successive difference. Annals of Mathematical Statistics, 1941, 12, 153-162.