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Kernel estimates (1997)
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About kernel estimates
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=======================Jose Silva, 18 Mar 1997==========ssc
From: camoes@mit.edu (Jose Fernando Camoes Mendonca Oliveira Silva)
Subject: Re: Kernel Estimates in SAS
Message-ID: <remove.this!camoes-ya02408000R1803972054380001@news.mit.edu>
Byberg wrote:
> SAS INSIGHT for WINDOWS95 has the capability to give Kernel
density estimates for a variable.
> SAS will graph the density estimate, give the smoothing parameter, give
the bandwidth, give the mode, and
> the AMISE. My question is what to do with this? What is the purpose of
this Kernel Estimator? What if I
> want to find an expected value and variance for this density? Any
insight into kernel densities or and
> references would be greatly appreciated.
Kernel densities are non-parametric estimates of the density, which is to
say an histogram on steroids :-) Seriously, a kernel density is a smooth
histogram and is useful when you don't know the functional form of a
distribution. It allows you to get a density function as a average of
kernels centered on the observation. The bandwidth is a measure of the
variance of these kernels that you are superimposing to create the
density.
Hausman and Newey have a recent econometrica paper on using this type of
estimator for deadweight loss estimation.
Bishop's "Neural networks for pattern recognition", Oxford has some stuff
on that. Also the forth volume of the Handbook of Econometrics, North
Holland has some stuff on that.
I have used Stata's kernel regression for some residual testing (to
show that it fails the normality assumption) and it come in handy
sometimes.
If you are going to use these, take note that:
1) As with most non-linear techniques kernel density estimation requires
a lot of observations to mean anything other than a good representation
of the stochastic disturbances in your process :-(
2) You have to set an optimal bandwidth. This is best done with cross
validation, where you minimize the mean square error of predicitions
on hold-out samples (ideally, the average over all observations of the
square error of prediction for that observation when it is held out
of the estimation process).
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