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st: RE: adaptive kernel density

From   "Nick Cox" <[email protected]>
To   <[email protected]>
Subject   st: RE: adaptive kernel density
Date   Fri, 14 Jan 2005 18:08:56 -0000

It is also possible to transform to logs, 
do the density estimation and then 
back-transform the density function using 
a standard probability result. This 
is an option in -mdensity- from SSC
and you could do it with official 
Stata with a few commands before and 
after. The results in practice might 
well resemble some adaptive method. 

In my experience the back-transformation 
is only helpful visually if the distribution
is moderately skew. With strong skewness 
it is often more practical to transform to 
logs and stay in log space. In the case 
of income people in this field seem very 
used to think about income on a log scale 

[email protected] 

Ramani Gunatilaka

> This is not a programming question but one on theory. I would 
> be grateful for any views about this.
> I am trying to decompose income inequality using DiNardo, 
> Fortin and Lemieux's (1996) semi-parametric methodology 
> (Econometrica 64(5), 1001-44) as applied to the kernel 
> density function.
> However, DiNardo et al, Deaton (Analysis of Household Surveys 
> - 1997) and D'ambrosio (Review of Income and Wealth 47(1), 
> 2001) transform the data into log-form and work with that.
> This is because the kernel estimator has difficulties 
> handling densities that have a high degree of asymmetry as is 
> the case with income data. Densities close to normality are 
> the easiest for the kernel estimator to estimate.
> Now my question is this:
> Would I be able to get round this problem of the kernel not 
> performing well if I were to estimate adaptive kernel density 
> (akdensity) on the original data?
> The adaptive kernel density curve, though smoother than the 
> kernel density function, is also skewed or asymmetric. 
> Wouldn't this matter?
> Would someone know of a useful reference in this regard?

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