Auxiliary functions (for internal use)

Function gethani determines a bandwidth that leads to, for the specified kernel, a variance reduction for a non-adaptive kernel estimate by a factor of value. getvofh calculates the sum of location weights for a given bandwidth vector and kernel. sofmchi precomputes the variance of a non-central chi distribution with 2*L degrees of freedom as a function of the noncentrality parameter for an interval c(0,to). Functions residualVariance and residualSpatialCorr are used in package fmri to calculate variances and spatial correlations from residual objects.

gethani(x, y, lkern, value, wght, eps = 0.01)
getvofh(bw, lkern, wght)
sofmchi(L, to = 50, delta = 0.01)
residualVariance(residuals, mask, resscale = 1, compact = FALSE)
residualSpatialCorr(residuals, mask, lags = c(5, 5, 3), compact = FALSE)

Arguments

x	lower bound of search interval
y	upper bound of search interval
lkern	code for location kernel
value	target sum of location weights
wght	relative size of voxel dimensions c(0,0) for 1D and c(w1,0) for 2D problems.
eps	attempted precision for bandwidth search
bw	vector of bandwidths, length equal to 1,2 or 3 depending on the dimensionality of the problem.
L	number of effective coils, 2*L is the degree of freedom of the non-central chi distribution.
to	upper interval bound.
delta	discretization width.
residuals	array of residuals, ifcompact only containing voxel with mask, otherwise for complete data cubes.
mask	mask of active voxel (e.g. brain masks)
resscale	scale for residuals (residuals may be scaled for optimal integer*2 storage)
compact	logical, determines if only information for voxel within mask or full for full data cubes is given.
lags	positive integer vector of length 3, maximum lags for spatial correlations for each coordinate direction to be computed

Details

These are auxiliary functions not to be used by the user. They are only exported to be available for internal use in packages fmri, dti, qMRI and adimpro.

Value

gethani returns a vector of bandwidths, getvofh returns the variance reduction that would be obtained with a kernel estimate employing the specified kernel and bandwidth, sofmchi returns a list with, e.g., components ncp and s2 containing vectors of noncentralityparameter values and corresponding variances, respectively, for the specified noncentral Chi distribution, residualVariance returns a vector (compact==TRUE) or array(compact==FALSE) of voxelwise residual variances, residualSpatialCorr returns an array of dimension lags containing spatial correlations.

Author

Joerg Polzehl polzehl@wias-berlin.de

Note

These functions are for internal use only. They are only exported to be available in other packages.