[Forum SIS] Bocconi DEC Seminar: Eric Gautier - November 18th

[Anna Simoni]

Dear colleagues, 



The Department of Decision Sciences (DEC) of Bocconi University is pleased to invite you to the seminar: 


================================================================== 

DEC Seminar 
Università Bocconi, 
Room 3-E4-SR03 
Via Rontgen 1 - 3rd floor 
Time: 12:30pm 


The DEC seminar schedule is available at http://www.unibocconi.eu/statseminar 

Thursday, November 18th 

Eric Gautier 
(CREST – ENSAE) 

"The IV selector: estimation and selection of the variables when the number of variables and instruments can be much larger than the sample size" 

We introduce and analyse a new instrumental variables estimation procedure 
for linear models containing endogenous regressors. It can handle 
a small sample size n and a large number of regressors, and even larger 
number of instruments L. Distributional assumptions on the error term 
or the distribution of the instruments and regressors are very mild. Under 
proper assumptions on the action of a matrix, relating the variables of the 
structural model and the instruments, on sparse vectors, and the assumption 
that the vector of coefficients in the structural model is sparse (or 
approximately sparse), it is possible to estimate the vector of coefficients 
even in cases where L is much larger than n.  The procedure is a variation 
on the Dantzig selector of Candµes and Tao (2007). We obtain nonasymptotic 
upper bounds on the estimation of the vector of coefficients in 
lp-norms that hold with probability close to 1. The price that is paid 
in the upper bound, for not knowing which coordinates are non zero, is a 
power of log(L). Under proper assumptions, a thresholded 
version of the IV-selector is able to simultaneously select the right nonzero 
coefficients with a probability close to 1. The estimation reduces to simple 
linear programming. The method is completely robust to weak instruments and 
there is no real issue in selecting instruments with the IV -selector. 
Taking all possible exogenous instruments (up to an exponential in the sample size!) 
Still leads to tight bounds around the true vector of parameters. Adding an 
instrument which is irrelevant incurs a loss of log(L)-log(L-1) in the 
constant multiplying the parametric rate. This is totally negligible compared 
to the potential gain in adding an instrument with some power. It is also robust to heteroscedastic errors. 

============================================================================== 

Sincerely, 
Anna Simoni 



--------------------------- 
Anna Simoni 
Assistant Professor 
Department of Decision Sciences 
Università Bocconi 
via Roentgen, 1 
20136 Milano - Italy 
Email: anna.simoni a unibocconi.it 
Webpage: http://faculty.unibocconi.eu/annasimoni/ 
-------------- parte successiva --------------
Un allegato HTML è stato rimosso...
URL: <http://www.stat.unipg.it/pipermail/sis/attachments/20101111/78613659/attachment.html>