The geometric constants for simultaneous confidence bands are computed,
as described in Sun and Loader (1994) (bias adjustment is not implemented
here). These are then passed to the crit function, which
computes the critical value for the confidence bands. The method requires both the weight diagrams l(x), the
derivative l'(x) and (in 2 or more dimensions) the second
derivatives l''(x).
These are implemented exactly for a constant bandwidth; that
is, alpha=c(0,h) for some h. For nearest
neighbor bandwidths, the computations are approximate and a warning
is produced.
The theoretical justification for the bands uses normality of
the random errors $e_1,\dots,e_n$ in the regression model,
and in particular the spherical symmetry of the error vector.
For non-normal distributions, and likelihood models, one relies
on central limit and related theorems.
Computation uses the product Simpson's rule to evaluate the
multidimensional integrals (The domain of integration, and
hence the region of simultaneous coverage, is determined by
the flim argument). Expect the integration to be slow in more
than one dimension. The mint argument controls the
precision.