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Maximization by parts in extremum estimation

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  • Yanqin Fan
  • Sergio Pastorello
  • Eric Renault
Abstract
In this paper, we present various iterative algorithms for extremum estimation in cases where direct computation of the extremum estimator or via the Newton–Raphson algorithm is difficult, if not impossible. While the Newton–Raphson algorithm makes use of the full Hessian matrix, which may be difficult to evaluate, our algorithms use parts of the Hessian matrix only, the parts that are easier to compute. We establish consistency and asymptotic efficiency of our iterative estimators under regularity and information dominance conditions. We argue that the economic interpretation of a structural econometric model will often allow us to give credibility to a well‐suited information dominance condition. We apply our algorithms to the estimation of the Merton structural credit risk model and to the Heston stochastic volatility option pricing model.

Suggested Citation

  • Yanqin Fan & Sergio Pastorello & Eric Renault, 2015. "Maximization by parts in extremum estimation," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 147-171, June.
    • Handle: RePEc:wly:emjrnl:v:18:y:2015:i:2:p:147-171
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    File URL: http://hdl.handle.net/10.1111/ectj.12046
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    Cited by:

    1. Chorro, Christophe & Guégan, Dominique & Ielpo, Florian & Lalaharison, Hanjarivo, 2018. "Testing for leverage effects in the returns of US equities," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 290-306.
    2. David T. Frazierz & Eric Renault, 2016. "Efficient Two-Step Estimation via Targeting," CIRANO Working Papers 2016s-16, CIRANO.
    3. Paolo Vidoni, 2021. "Boosting multiplicative model combination," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 761-789, September.
    4. Frazier, David T. & Renault, Eric, 2017. "Efficient two-step estimation via targeting," Journal of Econometrics, Elsevier, vol. 201(2), pages 212-227.
    5. Massimiliano Caporin & Riccardo (Jack) Lucchetti & Giulio Palomba, 2020. "Analytical Gradients of Dynamic Conditional Correlation Models," JRFM, MDPI, vol. 13(3), pages 1-21, March.
    6. Han, Hyojin & Khrapov, Stanislav & Renault, Eric, 2020. "The leverage effect puzzle revisited: Identification in discrete time," Journal of Econometrics, Elsevier, vol. 217(2), pages 230-258.
    7. Nikolaus Hautsch & Ostap Okhrin & Alexander Ristig, 2023. "Maximum-Likelihood Estimation Using the Zig-Zag Algorithm," Journal of Financial Econometrics, Oxford University Press, vol. 21(4), pages 1346-1375.

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