[Forum SIS] Avviso di seminario

[Francesca De Battisti]

Ilgiorno 21 febbraio dalle 12:30 alle 13:30,presso l’aula seminari del Dipartimento di Economia, Management e MetodiQuantitativi dell’Università di Milano (II piano, entrata da via Conservatorio,n. 7), Samantha Leorato (Departmentof Economics and Finance, University of Rome Tor Vergata) and Franco Peracchi (Department ofEconomics and Finance, University of Rome Tor Vergata, Department of Economics,Georgetown University, Einaudi Institute for Economics and Finance) terranno unseminario dal titolo: 

  

Distribution and Quantile Regressions  

  

Abstract    

Given a continuousrandom variable Y and a random vector X defined on the same probability space,the conditional distribution function (CDF) and the conditional quantilefunction (CQF) give rise to two competing approaches to the estimation of theconditional distribution of Y given X. One approach -- distribution regression-- is based on direct estimation of the conditional distribution function(CDF); the other approach -- quantile regression -- is instead based on directestimation of the conditional quantile function (CQF). Since the CDF and theCQF are generalized inverses of each other, estimates of any functional of thedistribution may be obtained by appropriately transforming the direct estimatesof the CDF and the CQ. Similarly, indirect estimates of the CQF and the CDF maybe obtained by taking the generalized inverse of the direct estimates. Contraryto the QR estimator, that typically refers to a conditional ALAD estimator,there is no unique choice for the DR estimator. One possibility is to define abinary choice model for any given threshold $y$ and the corresponding dummyvariable $\{Y\leq y\}$. This choice is particularly suited to comparisons withthe QR estimator, since, in the unconditional case, the two approaches areequivalent. 

Our paper focuseson comparing QR and DR approaches, and their performances in terms ofefficiency, both asymptotically and for finite samples. Asymptotic efficiencyis measured by asymptotic MSE of the rescaled estimators of the CDF (or of theCQF), where asymptotic MSE is the sum of the asymptotic variance and of thesquared asymptotic bias. Asymptotic bias is allowed to be nonzero, thus takinginto account some form of local misspecification of either the QR or the DRmodels. For the asymptotic variance, we show that the choice of the linkfunction used for DR estimation matters, and that under the most popular errordistributions (i.e. logistic and normal) the QR is uniformly more efficient (inexpectation). 

The finite sample performance is assessed by anextensive Monte Carlo exercise.   



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Francesca De Battisti
Dipartimento di Economia, Management e Metodi Quantitativi 
(III piano, studio n. 29)
Via Conservatorio 7
20122 - Milano
Tel: 02.50321464
Fax: 02.50321505
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