plot.tiltAfterBootstrap(x, plots=NULL, ..., omit = TRUE, minimumB=100)
"tiltAfterBootstrap"
"fs"
= plot functional vs statistic
"fp"
= functional vs probabilities,
"sp"
= statistic vs probabilities
"pairs"
= pairwise scatterplots of many quantities.
The default is
"fs"
if
x
contains statistics,
else
"pairs"
.
TRUE
(the default), then points with effective sample size
smaller than
minimumB
are omitted from the plots.
Suppose one were to modify the original empirical distribution by placing unequal weights on the observations. As the weights change, both the statistic calculated from the weighted distribution, and the bootstrap distribution obtained by sampling with probabilities equal to those weights, change. Bootstrap tilting looks at the relationships between the statistic and summaries ("functionals") of the bootstrap distribution, as the weights change. In particular, the weights are selected by exponential or maximum likelihood tilting; these approximately maximize the change in the statistic given the distance (forward or backward Kullback-Leibler distance) between the weights and the original equal weights.
Assuming that the weighted statistic can be calculated, the most generally useful plot is of the functional (such as quantiles of the weighted bootstrap distribution) against the weighted statistics.
For example, when considering use of a inference procedure such as t-tests or confidence intervals that assumes that standard errors are independent of the statistic, it is useful to check that assumption by plotting either "Centered Quantiles" or "SE" (standard error) against the statistic.
Hesterberg, T.C. (2001), "Bootstrap Tilting Diagnostics"
x <- qgamma(ppoints(19), shape = 0.5) # artificial skewed data boot <- bootstrap(x, mean) tab <- tiltAfterBootstrap(boot) plot(tab) plot(tab, plots = "probs") plot(tab, plots = "pairs")