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Quasi-maximum likelihood estimation for conditional quantiles

Komunjer, Ivana (2005) Quasi-maximum likelihood estimation for conditional quantiles. Journal of Econometrics, 128 (1). pp. 137-164. ISSN 0304-4076. doi:10.1016/j.jeconom.2004.08.010.

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In this paper, we construct a new class of estimators for conditional quantiles in possibly misspecified nonlinear models withtime series data. Proposed estimators belong to the family of quasi-maximum likelihood estimators (QMLEs) and are based on a new family of densities which we call ‘tick-exponential’. A well-known member of the tick-exponential family is the asymmetric Laplace density, and the corresponding QMLE reduces to the Koenker and Bassett’s (Econometrica 46 (1978) 33) nonlinear quantile regression estimator. We derive primitive conditions under which the tick-exponential QMLEs are consistent and asymptotically normally distributed withan asymptotic covariance matrix that accounts for possible conditional quantile model misspecification and which can be consistently estimated by using the tick-exponential scores and Hessian matrix. Despite its non-differentiability, the tickexponential quasi-likelihood is easy to maximize by using a ‘minimax’ representation not seen in the earlier work on conditional quantile estimation.

Item Type:Article
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URLURL TypeDescription ItemEarlier version published as Social Science Working Paper 1139
Additional Information:© 2004 Elsevier B.V. All rights reserved. Received 29 June 2004. Formerly SSWP 1139.
Subject Keywords:Tick-exponential family; Minimax representation; QMLE; Conditional quantiles; Asymptotic distribution; Misspecification
Issue or Number:1
Classification Code:JEL: C22; C51; C61
Record Number:CaltechAUTHORS:20171106-140541830
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82989
Deposited By: Jacquelyn Bussone
Deposited On:07 Nov 2017 18:27
Last Modified:15 Nov 2021 19:54

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