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Quasi-Maximum Likelihood Estimation for Conditional Quantiles

Komunjer, Ivana (2002) Quasi-Maximum Likelihood Estimation for Conditional Quantiles. Social Science Working Paper, 1139. California Institute of Technology , Pasadena, CA.

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In this paper we derive the asymptotic distribution of a new class of quasi-maximum likelihood estimators (QMLE) based on a ‘tick-exponential’ family of densities. We show that the ‘tick-exponential’ assumption is a necessary and sufficient condition for a QMLE to be consistent for the parameters of a correctly specified model of a given conditional quantile. Hence, the role of this family of densities in the conditional quantile estimation is analog to the role of the linear-exponential family in the conditional mean estimation. The ‘tick-exponential’ QMLEs are shown to be asymptotically normal with an asymptotic covariance matrix that has a novel form, not seen in earlier work, and which accounts for possible model misspecification. For practical purposes, we show that the maximization of the ‘tick-exponential’ (quasi) log-likelihood can conveniently be carried out by using standard gradient-based optimization techniques. More importantly, we provide a consistent estimator for the asymptotic covariance matrix based on the “scores” of the log-likelihood, which allows us to compute the conditional quantile confidence intervals.

Item Type:Report or Paper (Working Paper)
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URLURL TypeDescription ItemLater version published in Journal of Econometrics
Additional Information:Paper presented at the 2002 Summer Meeting of the Econometric Society, UCLA. I am indebted to Graham Elliott, Philip Gill, Alain Monfort, Christopher Sims, Gary Solon and Hal White for their suggestions and comments. Published as Komunjer, I. (2005). Quasi-maximum likelihood estimation for conditional quantiles. Journal of Econometrics, 128(1), 137-164.
Group:Social Science Working Papers
Subject Keywords:‘tick-exponential’ densities, conditional quantiles, quasi-maximum likelihood estimation, misspecification, asymptotic distribution
Series Name:Social Science Working Paper
Issue or Number:1139
Classification Code:JEL: C13, C20, C51, C63
Record Number:CaltechAUTHORS:20170802-144322831
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79780
Deposited By: Jacquelyn Bussone
Deposited On:02 Aug 2017 23:48
Last Modified:03 Oct 2019 18:23

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