Public Lectures on Structural Econometrics - CEMMAP masterclass - Shared screen with speaker view
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Is a factor of 1/2 missing in the 2nd line?
@Kevin: are you satisfied with Bob's explanation?
It looks like it.
the formula for fx^(N) (x) looks very similar with f(x,y)=f(x)f(y). Why is this still true when x_1 and x_k are not independent?
y and x are not assumed to be independent. f(y,x)/f(x) = f(y|x)
Then the integral of y*f(y|x) dy gives E(y|x)
@Zhuotong, are you asking about why the product kernel is used in the multi-variate case?
Zhuotong is referring to the two-dimensional kernel fn I think
sum of product =/= product of sum
yes. the formula in page 5
@Zhuotong, that is a common way to handle multivariate kernel regression. It's simpler than using a more general multivariate kernel. It does not require the variables to be independent from each other.
The main reason is for simplicity as I understand it.
@Zhuotong: Bob is going over it now. Let us know if it still not clear after this slide
It's a way to measure the distance between x_n and x.
I see. Thanks a lot!
I am not familar with the estimators of eq (2) and (3). Is there any reference I can read more about them? Thank you?
I don't know on top of my head, but, unless others have one, we can ask him maybe at the end of the class, what do you think?
Sounds good. Thank you, Joan.
No problem! Remind us if we forget!
is this equivalent to Frisch Waugh Lovell theorem
@Vladimir: if you wish, it is the analogue in a way in this partially linear model. The function g(z) here is unknown
I would say, Vladimir, the intuition would be the same indeed
Is g known here?
@Kevin, it is unknown.
@Kevin: it is a special monotonic version of the previous partially linear model -- g(.) is monotone
Is eq (8) identified if you have x in both par and nonpar parts?
@Shunan: it depends on the restrictions you place on g(.). I believe Bob will take about this but … please ask more if this is not the case!
Note that before the covariates were partitioned in x and z. Now they are not but we are placing a strong restriction on g(.) we did not before. There is certainly a trade-off
Dole, D. (1999): “Cosmo: A Constrained Scatterplot Smoother for Estimating Convex,Monotonic Transformations,” Journal of Business & Economic Statistics, 17, 444–455
this is what I had in mind in case anyone is interested
@Elena, thank you.
WRIGHT, F. T. (1981), “The Asymptotic Behavior of Monotone Regression Estimates”,Annals of Statistics,9, 443–448