# st: correction: estimating the average slope and its standard error in anon-parametric regression

 From "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" <[email protected]> To "'[email protected]'" <[email protected]> Subject st: correction: estimating the average slope and its standard error in anon-parametric regression Date Wed, 22 Dec 2004 13:05:07 -0600

```oops! - I just realized the standard error I gave would be for using the
data points, not the estimated function at the endpoints. So the standard
error variance should more properly be

Var(f_hat(b)-f_hat(a))/(b-a)^2

where f_hat( ) is the fitted function.

The numerator is Var(f_hat(b)+Var(f_hat(a))-2*cov(f_hat(b), f_hat(a))

I see where using predict with the stdp option would give you the two
variances, but I'm not sure how to get the covariance. Or if you can write
out an explicit expression for f_hat(b) and f_hat(a), you could use lincom
or nlcom to get its standard error.

Al Feiveson

-----Original Message-----
From: [email protected]
[mailto:[email protected]]On Behalf Of FEIVESON, ALAN
H. (AL) (JSC-SK) (NASA)
Sent: Wednesday, December 22, 2004 12:55 PM
To: '[email protected]'
Subject: st: RE: estimating the average slope and its standard error in
anon-parametric regression

The average slope of any continuous function f on an interval (a, b) is
(f(b)-f(a))/(b-a)
Its standard error would then be 2*Var(e)/(b-a)^2

Al Feiveson

-----Original Message-----
From: [email protected]
[mailto:[email protected]]On Behalf Of Marco Leonardi
Sent: Wednesday, December 22, 2004 3:47 AM
To: [email protected]
Subject: st: estimating the average slope and its standard error in
anon-parametric regression

Greetings,

I estimate a non parametric regression of the form y=g(x)+e using the STATA
command kernreg.

I am interested in the "slope" of the regression line g'(x), that is the
marginal effect on the conditional expectation g(x)=E(y|x) of a change in x.
Obviously the slope changes over the range of x.

Is there a simple way to estimate the average slope d=E[g'(x)] and its
standard error?

Many thanks

Marco Leonardi
Dipartimento Studi del Lavoro
Universit� degli Studi di Milano
Via Conservatorio 7
20122 Milano
tel: +39 02 50321162

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