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Re: st: RE: -locpoly-

From (Jeff Pitblado, StataCorp LP)
Subject   Re: st: RE: -locpoly-
Date   Tue, 01 Jun 2004 13:59:40 -0500

For some reason my original reply did not go through:

"D.Christodoulou" <> asks about some details behind

> Following Nick's reply on my previous posting I was not able to locate the
> reference:

> Fan, Fan, and Gijbels,  "Local Polynomial Modelling and Its Applications",
> in Monographs of Statistics and Applied Probability, Chapman and Hall/CRC.

I'm not sure if this helps, but this is number 66 in the series.

	Fan, J. and I. Gijbels.  1996.  Local Polynomial Modelling and Its
	Applications.  Chapman & Hall: London.

I was able to find it by searching on "fan gijbles" at a couple of on-line

> (1) I would like ask the authors of the -locpoly- command and whoever is
> familiar with the command whether the following references are sufficient
> in explaining the algorithm of -locpoly-:

> Hardle (1990), Applied Nonparametric Regression, Econometric Society
> Monographs, Cambridge Press.

> Cleveland (1979), "Robust Locally Weighted Regression and Smoothing
> Scatterplots", Journal of the American Statistical Association, Vol.74,
> No.368, pp.829-836.

> Muller (1987), "Weighted Local Regression and Kernel Methods for
> Nonparametric Fitting", Journal of the American Statistical Association,
> Vol.82, No.397, pp.231-238.

The above three references are cited in Fan and Gibjbels.  D.Christodoulou
might want to start with Cleveland (1979).

> (2) Has anyone written something on nonparametric smoothing for
> higher-dimensions, i.e. more than one explanatory variables ?

I am not aware of anything written for Stata that handles this case.

> (3) How can I statistically compare (given a confidence level) the
> parametric fit "y-hat" with the non-parametric fit "conditional-y-mean" ?
> Has anyone written a statistical test such as the one described in
> Hardle(1990, ch.9.3) for the qsuared deviation between the two measures ?

This is a good research question worth a literature search.  Simonoff has some
discussion of goodnetss-of-fit:

	Simonoff, J. S.  1996.  Smoothing Methods in Statistics.  Springer:
	New York.

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