varDiff: Estimation of scale based on sequential-order differences

In HenrikBengtsson/matrixStats: Functions that Apply to Rows and Columns of Matrices (and to Vectors)

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)

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.

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.

Value

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

Author(s)

Henrik Bengtsson

References

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

See Also

For the corresponding non-differentiated estimates, see var, sd, mad and IQR. Internally, diff2() is used which is a faster version of diff().

HenrikBengtsson/matrixStats documentation built on Nov. 15, 2024, 3:20 p.m.