I would like to experiment with testing the fit of a loess model against
the fit from an ordinary linear regression. The 1988 JASA paper by
Cleveland and Devlin *appears* to indicate that this can be done, at
least ``approximately''. They, as I read it, advocate the use of an
ANOVA type test with degree of freedom chosen to make the ``F ratio''
have an approximate F distribution under the null hypothesis.
(I have the impression that the approximate F distribution approach
has its sceptics in other contexts, but let's not go there for now,
please.)
The problem for me is that the degrees of freedom values involve the
trace of (I - L)(I - L)' --- where L is the matrix effecting the loess
fit, i.e. yhat = Ly --- and other trace expressions involving the
difference
between (I - L)(I - L)' and the corresponding expression for the
linear model.
The linear model bits I can handle. How do I/can I get at L from the
output
of loess?
Or is there some other approach that I can use, involving quantities
that are
directly accessible from the loess object? How? Which quantities? Can
anyone give me a fairly simple step by step recipe?
A Monte Carlo approach (parametric or non-parametric bootstrapping)
would seem to be
quite feasible, but I thought I'd look for an ``analytic'' approach
first.
Thanks for any help that anyone can give.
cheers,
Rolf Turner
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