R: Estimation of scale based on sequential-order differences

varDiff {matrixStats}

R Documentation

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

`x`	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`, `NA`s 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.

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.