Plots for tiltAfterBootstrap

DESCRIPTION:

Selection of plots related to tilting-after-bootstrap

USAGE:

plot.tiltAfterBootstrap(x, plots=NULL, ...,  
    omit = TRUE, minimumB=100) 

REQUIRED ARGUMENTS:

x
an object of class "tiltAfterBootstrap"

OPTIONAL ARGUMENTS:

plots
character vector, containing one or more of "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".
...
additional arguments to pass to plotting commands , , and .
omit
if TRUE (the default), then points with effective sample size smaller than minimumB are omitted from the plots.
minimumB
integer, minimum acceptable bootstrap sample size; points that fail to meet this are not plotted.

SIDE EFFECTS:

This creates plots on the current graphics device.

DETAILS:

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.

REFERENCES:

Hesterberg, T.C. (2001), "Bootstrap Tilting Diagnostics"

SEE ALSO:

The objects are created by , operating on an object created by . The underlying plot functions are , , and .

EXAMPLES:

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")