Quasi-Maximum Likelihood Estimation for Conditional Quantiles
- Creators
- Komunjer, Ivana
Abstract
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.
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.Attached Files
Published - sswp1139.pdf
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Additional details
- Eprint ID
- 79780
- Resolver ID
- CaltechAUTHORS:20170802-144322831
- Created
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2017-08-02Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field
- Caltech groups
- Social Science Working Papers
- Series Name
- Social Science Working Paper
- Series Volume or Issue Number
- 1139