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A SIMPLE ITERATIVE Z-ESTIMATOR FOR SEMIPARAMETRIC MODELS

Published online by Cambridge University Press:  12 April 2018

David T. Frazier
David T. Frazier*
Affiliation:
Monash University
*
*Address correspondence to David Frazier, Department of Econometrics and Business Statistics, Monash University, Melbourne, Australia; e-mail: david.frazier@monash.edu.
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Abstract

We propose a new iterative estimation algorithm for use in semiparametric models where calculation of Z-estimators by conventional means is difficult or impossible. Unlike a Newton–Raphson approach, which makes use of the entire Hessian, this approach only uses curvature information associated with portions of the Hessian that are relatively easy to calculate. Consistency and asymptotic normality of estimators obtained from this algorithm are established under regularity conditions and an information dominance condition. Two specific examples, a quantile regression model with missing covariates and a GARCH-in-mean model with conditional mean of unknown functional form, demonstrate the applicability of the algorithm. This new approach can be interpreted as an extension of the maximization by parts estimation approach to semiparametric models.

Type
ARTICLES
Information
Econometric Theory , Volume 35 , Issue 1 , February 2019 , pp. 111 - 141
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

This article has benefited tremendously from the feedback provided by two anonymous referees and a co-editor. Additional thanks are given to Eric Renault, Mervyn Silvapulle, Saraswata Chaudhuri, Yanqin Fan, Dennis Kristensen, and Oliver Linton.

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