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, ..., useNames = TRUE)
colVarDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ..., useNames = TRUE)
rowSdDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ..., useNames = TRUE)
colSdDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ..., useNames = TRUE)
rowMadDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ..., useNames = TRUE)
colMadDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ..., useNames = TRUE)
rowIQRDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ..., useNames = TRUE)
colIQRDiffs(x, rows = NULL, cols = NULL, na.rm = FALSE, diff = 1L,
  trim = 0, ..., useNames = TRUE)

Value

Returns a numeric

vector of length 1, length N, or length K.

Arguments

x: A numeric vector of length N or a numeric NxK matrix.
idxs: A vector indicating subset of elements to operate over. If NULL, no subsetting is done.
na.rm: If TRUE, missing values are excluded.
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.
rows: A vector indicating subset of rows to operate over. If NULL, no subsetting is done.
cols: A vector indicating subset of columns to operate over. If NULL, no subsetting is done.
useNames: If TRUE (default), names attributes of the result are set, otherwise not.

Author

Henrik Bengtsson

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.