[R] gefp() boundaries?

[Achim Zeileis]

On Fri, 7 Oct 2011, bonda wrote:

> Well, I am still confused... shouldn't the "made-by-hands"-process (correctly
> constructed, of course) and the gefp()-process be similar?

Correctly constructed yes. And if unsure, just read the source code (as 
previously suggested): it's open!

> For the case of efp()-process it has been worked, at least... Besides, 
> I'd like to know: 1) if I have the gefp()-process (scaled to unit 
> interval [0;1]), can I get the unscaled one for the interval [0;n]?

Make your data a "ts" series with the desired index or use the order.by 
argument of gefp().

> 2) is it possible to define a type of the score process like this was in
> efp()? I could find that neither in ?gefp, nor in CSDA-paper-2006.

The 2005 Econ Rev paper on ?gefp explains how various types of processes 
are special cases of the gefp framework by setting suitable functionals.

> The example was bad and incorrect, the another one:
>
> data("BostonHomicide")
>
> gprocess <- gefp(homicides ~ ahomicides25, family = poisson, data =
> BostonHomicide);
>
> my.model <- glm(homicides ~ ahomicides25, family = poisson, data =
> BostonHomicide);
> J <- vcov(my.model);

This is (a) not what the paper says, (b) not on the right scale.

> J.sqrinv <- solve(sqrtm(J))/n;
> my.psi <- estfun(my.model);
> my.process <- apply(as.matrix(my.psi), 2, cumsum)%*%t(J.sqrinv)/sqrt(n);

It's really not that difficult. All equations below pertain to the CSDA 
paper:

## fit model
fm <- glm(homicides ~ ahomicides25, family = poisson,
   data = BostonHomicide)
n <- nobs(fm)

## Equation 2
W <- apply(estfun(fm), 2, cumsum) / sqrt(n)

## Equation 3
J <- crossprod(estfun(fm)) / n

## Equation 4
efp1 <- W %*% solve(root.matrix(J))

## via gefp()
efp2 <- gefp(fm, fit = NULL)$process

## using information matrix instead of OPG
efp3 <- W %*% root.matrix(vcov(fm) * n)

## visualize everything
plot(merge(efp2[-1,], efp1, efp3),
   screen = rep(1:2, 3), col = rep(1:3, each = 2))

The green lines pertain to the model with the alternative estimator of the 
covariances and is hence somewhat different.
Z

> Regards,
> Julia
>
>
>
>
>
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