### Name: Imp.Estimates
### Title: Importance Sampling Estimates
### Aliases: Imp.Estimates imp.moments imp.prob imp.quantile imp.reg
### Keywords: htest nonparametric

### ** Examples

# Example 9.8 of Davison and Hinkley (1997) requires tilting the 
# resampling distribution of the studentized statistic to be centred 
# at the observed value of the test statistic, 1.84.  In this example
# we show how certain estimates can be found using resamples taken from
# the tilted distribution.
grav1 <- gravity[as.numeric(gravity[,2])>=7,]
grav.fun <- function(dat, w, orig)
{    strata <- tapply(dat[, 2], as.numeric(dat[, 2]))
     d <- dat[, 1]
     ns <- tabulate(strata)
     w <- w/tapply(w, strata, sum)[strata]
     mns <- tapply(d * w, strata, sum)
     mn2 <- tapply(d * d * w, strata, sum)
     s2hat <- sum((mn2 - mns^2)/ns)
     as.vector(c(mns[2]-mns[1],s2hat,(mns[2]-mns[1]-orig)/sqrt(s2hat)))
}
grav.z0 <- grav.fun(grav1,rep(1,26),0)
grav.L <- empinf(data=grav1, statistic=grav.fun, stype="w", 
                 strata=grav1[,2], index=3, orig=grav.z0[1])
grav.tilt <- exp.tilt(grav.L,grav.z0[3],strata=grav1[,2])
grav.tilt.boot <- boot(grav1, grav.fun, R=199, stype="w", 
                       strata=grav1[,2], weights=grav.tilt$p,
                       orig=grav.z0[1])
# Since the weights are needed for all calculations, we shall calculate
# them once only.
grav.w <- imp.weights(grav.tilt.boot)
grav.mom <- imp.moments(grav.tilt.boot, w=grav.w, index=3)
grav.p <- imp.prob(grav.tilt.boot, w=grav.w, index=3, t0=grav.z0[3])
grav.q <- imp.quantile(grav.tilt.boot, w=grav.w, index=3, 
                       alpha=c(0.9,0.95,0.975,0.99))