Usage:

kappa0(formula, cov=0.95, ...)

Arguments:

formula

Local regression model formula.

cov

Coverage Probability for critical values.

ldots

Other arguments to locfit.

Description:

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 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.

The theoretical justification for the bands are computed using the spherical symmetry of the Normal distributions. 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. Expect this to be slow in more than one dimension. The mint argument controls the precision.

Value:

A list with components for the critical value, geometric constants, e.t.c. Can be passed directly to plot.locfit as the crit argument.

See Also:

locfit, plot.locfit, crit, crit<-.

Examples:

# 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")

References:

Sun, J. and Loader, C. (1994). Simultaneous confidence bands for linear regression and smoothing. Annals of Statistics 22, 1328-1345.

Key Words:

locfit