imp.weights {boot} | R Documentation |

## Importance Sampling Weights

### Description

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`

.

### Usage

```
imp.weights(boot.out, def = TRUE, q = NULL)
```

### Arguments

`boot.out` |
A object of class |

`def` |
A logical variable indicating whether the defensive mixture distribution
weights should be calculated. This makes sense only in the case where the
replicates in |

`q` |
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. |

### Details

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`

.

### Value

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`

.

### Note

See the example in the help for `imp.moments`

for an example of using
`imp.weights`

.

### References

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.

### See Also

`boot`

, `exp.tilt`

, `imp.moments`

, `smooth.f`

, `tilt.boot`

*boot*version 1.3-30 Index]