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st: RE: trying to understand -lpoly- with degree zero


From   philippe van kerm <philippe.vankerm@ceps.lu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: trying to understand -lpoly- with degree zero
Date   Tue, 13 Apr 2010 09:11:22 +0200

Dan,

The kernel function you are using is what Stata would typically refer to as the 'alternative Epanechnikov kernel'. See under -kdensity- in the manual for kernel definitions.

Try adding the -kernel(epan2)- option to your -lpoly- call.

Philippe


> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Dan Weitzenfeld
> Sent: Tuesday, April 13, 2010 1:20 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: trying to understand -lpoly- with degree zero
>
> Hi All,
> I'm trying to reverse-engineer the lpoly command, so that I can code it
> in a different language.
> Specifically, I'm trying to mimic the command with the default options
> of degree(0) and kernel(epanechnikov).
> Within -help lpoly-, it says:
>
>
>     degree(#) specifies the degree of the polynomial to be used in the
> smoothing.  The default is degree(0), meaning local-mean
>         smoothing.
>
> I understand this to mean that at each point in the smoothing grid, a
> kernel-weighted mean is taken.  For my purposes, it makes sense to use
> every point in the dataset as a point in the grid.  But when I tried to
> code that - see below - my resulting curve is less smooth than the
> output of -lpoly- with degree 0, same kernel, same half-width.
>
> According to wikipedia, the epanechnikov kernel is:
> K(u) = (3/4)(1-u^2)
> Am I scaling the kernel incorrectly?
>
> Thanks in advance,
> Dan
>
> *----------------------------------------------------
>
> webuse motorcycle, clear
> *my dataset is a constant 60 hz; changing this dataset to mimic
> replace time = _n*(1/60)
> local  halfwidth = .04
> local  halfwidth_squared = `halfwidth'*`halfwidth'
> qui gen fake_lpoly = .
> qui count
> local vals = r(N)
> forvalues i = 1(1)`vals' {
>  local time = time[`i']
>  capture drop distance* kernel product
>  qui gen distance_from_point = time-`time'
>  qui gen distance_sq =  distance_from_point*distance_from_point
> *generating epanechnikov kernel, scaled to local halfwidth
>  qui gen kernel = (3/4)*(1- (distance_sq/`halfwidth_squared'))
>  qui gen product = kernel*accel if kernel>=0
>  qui sum product
>  local numerator = r(sum)
>  qui sum kernel if kernel>=0
>  local denominator = r(sum)
>  qui replace fake_lpoly = `numerator'/`denominator' in `i'
> }
>
> *compare with -LPOLY-
> sort time
> capture drop x real_lpoly
> lpoly accel time, bw(`halfwidth') n(`vals') gen(x real_lpoly) nogra
> twoway (line  real_lpoly  fake_lpoly time) (scatter  accel time)
>
> *--------------------------------------------------
>
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