This function calculates the importance sampling weight required to correct
for simulation from a distribution with probabilities p when estimates
are required assuming that simulation was from an alternative distribution
with probabilities q.
imp.weights(boot.out, def = TRUE, q = NULL)A vector of importance weights of the same length as boot.out$t. These
weights can then be used to reweight boot.out$t so that estimates can be
found as if the simulations were from a distribution with probabilities q.
A object of class "boot" generated by boot or tilt.boot. Typically the
bootstrap simulations would have
been done using importance resampling and we wish to do our calculations
under the assumption of sampling with equal probabilities.
A logical variable indicating whether the defensive mixture distribution
weights should be calculated. This makes sense only in the case where the
replicates in boot.out were simulated under a number of different
distributions. If this is the case then the defensive mixture weights use a
mixture of the distributions used in the bootstrap. The alternative is to
calculate the weights for each replicate using knowledge of the distribution
from which the bootstrap resample was generated.
A vector of probabilities specifying the resampling distribution from which
we require inferences to be made. In general this would correspond to the usual
bootstrap resampling distribution which gives equal weight to each of the
original observations and this is the default. q must have length equal
to the number of observations in the boot.out$data and all elements of q
must be positive.
The importance sampling weight for a bootstrap replicate with frequency
vector f is given by prod((q/p)^f). This reweights the replicates so that
estimates can be found as if the bootstrap resamples were generated according
to the probabilities q even though, in fact, they came from the
distribution p.
Davison, A. C. and Hinkley, D. V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.
Hesterberg, T. (1995) Weighted average importance sampling and defensive mixture distributions. Technometrics, 37, 185--194.
Johns, M.V. (1988) Importance sampling for bootstrap confidence intervals. Journal of the American Statistical Association, 83, 709--714.
boot, exp.tilt, imp.moments, smooth.f, tilt.boot