Pivotal statistics, for bootstrap-t confidence intervals

DESCRIPTION:

These functions are input to and consist of a list of two functions, pivot and inverse.

USAGE:

resampPivotT 
resampPivotDiff 
resampPivotRatio 
   each have two components, functions with these arguments: 
pivot(replicates, observed) 
inverse(observed, quantiles) 

REQUIRED ARGUMENTS:

replicates
a matrix with B rows (the number of bootstrap samples) and k columns; the replicates component of a bootstrap object.
observed
a vector of length k; the observed component of a bootstrap object.
quantiles
matrix with K rows and r columns, where r is the number of parameters for which intervals are desired.

VALUE:

The pivot function returns a matrix with B rows and K columns.

the inverse function returns a matrix with K rows and r columns.

For bootstrap-T intervals for the means of multivariate data with p columns, k=2p (means and standard errors for each column) K=p (t-statistics for each column), and r=p (confidence intervals for each column). If intervals were desired for only certain columns of the data, then K and r could be smaller.

DETAILS:

resampPivotT$pivot calculates
(bootstrap estimates - observed estimates) / standardErrors

for each bootstrap sample. Then bootstrapT calculates quantiles of the bootstrap distribution of this pivotal quantity and calls resampPivotT$inverse, which solves
(observed estimates - parameters) / (observed standardErrors)
for the parameter values.

For multivariate statistics those calculations are performed for each column, assuming that the estimates are in positions 1, 3, ... (these columns of replicates and positions in observed) and the standard errors in positions 2, 4, ...

The corresponding pivots for resampPivotDiff and resampPivotRatio are
bootstrap estimates - observed estimates
bootstrap estimates / observed estimates
respectively.

See code of resampPivotT, resampPivotDiff or resampPivotRatio for examples, if you write your own pair of functions.

SEE ALSO:

for examples which use these functions.