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

 From Dan Weitzenfeld To "statalist@hsphsun2.harvard.edu" Subject st: trying to understand -lpoly- with degree zero Date Mon, 12 Apr 2010 18:19:56 -0500

```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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