kappa0 {locfit}  R Documentation 
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,...,e_n in the regression model, and in particular the spherical symmetry of the error vector. For nonnormal 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.
kappa0(formula, cov=0.95, ...)
formula 
Local regression model formula. A "locfit" object can also
be provided; in this case the formula and other arguments are extracted
from this object.

cov 
Coverage Probability for critical values. 
... 
Other arguments to locfit . Important arguments
include flim and alpha . 
A list with components for the critical value, geometric constants,
e.t.c. Can be passed directly to plot.locfit
as the
crit
argument.
Sun, J. and Loader, C. (1994). Simultaneous confidence bands for linear regression and smoothing. Annals of Statistics 22, 13281345.
locfit
, plot.locfit
,
crit
, crit<
.
# compute and plot simultaneous confidence bands data(ethanol) fit < locfit(NOx~E,data=ethanol) crit(fit) < kappa0(NOx~E,data=ethanol) plot(fit,crit=crit,band="local")