Critical Values for Simultaneous Confidence Bands.
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. 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 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.
kappa0(formula, cov=0.95, ev=lfgrid(20), ...)
formula |
Local regression model formula. A |
cov |
Coverage Probability for critical values. |
ev |
Locfit evaluation structure. Should usually be a grid – this specifies the integration rule. |
... |
Other arguments to |
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, 1328-1345.
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")
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