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Some Convergence Theory For Iterative Estimation Procedures With An Application To Semiparametric Estimation

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  • Dominitz, Jeff
  • Sherman, Robert P.

Abstract

We develop general conditions for rates of convergence and convergence in distribution of iterative procedures for estimating finite-dimensional parameters. An asymptotic contraction mapping condition is the centerpiece of the theory. We illustrate some of the results by deriving the limiting distribution of a two-stage iterative estimator of regression parameters in a semiparametric binary response model. Simulation results illustrating the computational benefits of the first-stage iterative estimator are also reported.We thank a co-editor and two referees for comments and criticisms that led to significant improvements in this paper. We also thank Roger Klein for providing us with Gauss code to compute his estimator.

Suggested Citation

  • Dominitz, Jeff & Sherman, Robert P., 2005. "Some Convergence Theory For Iterative Estimation Procedures With An Application To Semiparametric Estimation," Econometric Theory, Cambridge University Press, vol. 21(4), pages 838-863, August.
    • Handle: RePEc:cup:etheor:v:21:y:2005:i:04:p:838-863_05
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    1. Shakeeb Khan & Xiaoying Lan & Elie Tamer & Qingsong Yao, 2021. "Estimating High Dimensional Monotone Index Models by Iterative Convex Optimization1," Papers 2110.04388, arXiv.org, revised Feb 2023.
    2. Fermanian, Jean-David & Lopez, Olivier, 2018. "Single-index copulas," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 27-55.
    3. Guang Cheng, 2013. "How Many Iterations are Sufficient for Efficient Semiparametric Estimation?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 592-618, September.
    4. Jiang, Bin & Yang, Yanrong & Gao, Jiti & Hsiao, Cheng, 2021. "Recursive estimation in large panel data models: Theory and practice," Journal of Econometrics, Elsevier, vol. 224(2), pages 439-465.
    5. Hacioglu Hoke, Sinem & Kapetanios, George, 2017. "Common correlated effect cross-sectional dependence corrections for non-linear conditional mean panel models," Bank of England working papers 683, Bank of England.
    6. Knobel, Alexander (Кнобель, Александр) & Chentsov, Alexander (Ченцов, Александр), 2018. "The Impact of Exchange Rates and Their Volatility on Russia's Foreign Trade, Taking into Account its Membership in EAEU [Влияние Обменных Курсов И Их Волатильности На Внешнюю Торговлю России С Учет," Working Papers 061824, Russian Presidential Academy of National Economy and Public Administration.
    7. Christophe Bellégo & David Benatia & Louis-Daniel Pape, 2022. "Dealing with Logs and Zeros in Regression Models," Working Papers 2022-08, Center for Research in Economics and Statistics.
    8. Dias, Gustavo Fruet & Kapetanios, George, 2018. "Estimation and forecasting in vector autoregressive moving average models for rich datasets," Journal of Econometrics, Elsevier, vol. 202(1), pages 75-91.
    9. Norris Keiller, Agnes & de Paula, Aureo & Van Reenen, John, 2024. "Production function estimation using subjective expectations data," CEPR Discussion Papers 19259, C.E.P.R. Discussion Papers.
    10. David T. Frazierz & Eric Renault, 2016. "Efficient Two-Step Estimation via Targeting," CIRANO Working Papers 2016s-16, CIRANO.
    11. Roberta Distante & Elena Verdolini & Massimo Tavoni, 2016. "Distributional and Welfare Impacts of Renewable Subsidies in Italy," Working Papers 2016.36, Fondazione Eni Enrico Mattei.
    12. 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.
    13. Tadao Hoshino, 2013. "Estimation of the preference heterogeneity within stated choice data using semiparametric varying-coefficient methods," Empirical Economics, Springer, vol. 45(3), pages 1129-1148, December.
    14. Yan Cui & Qi Li & Fukang Zhu, 2020. "Flexible bivariate Poisson integer-valued GARCH model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1449-1477, December.
    15. Song, Ze & Li, Lianyou & Ma, Chao, 2013. "The EASI Demand System : Evidence from China Household," MPRA Paper 48435, University Library of Munich, Germany.
    16. Hiroaki Kaido & Kaspar Wüthrich, 2021. "Decentralization estimators for instrumental variable quantile regression models," Quantitative Economics, Econometric Society, vol. 12(2), pages 443-475, May.
    17. Christopher D. Walker, 2024. "Semiparametric Bayesian Inference for a Conditional Moment Equality Model," Papers 2410.16017, arXiv.org.
    18. Frazier, David T. & Renault, Eric, 2017. "Efficient two-step estimation via targeting," Journal of Econometrics, Elsevier, vol. 201(2), pages 212-227.
    19. Bruce E. Hansen & Seojeong Jay Lee, 2018. "Inference for Iterated GMM Under Misspecification and Clustering," Discussion Papers 2018-07, School of Economics, The University of New South Wales.
    20. Sinem Hacıoğlu Hoke & George Kapetanios, 2021. "Common correlated effect cross‐sectional dependence corrections for nonlinear conditional mean panel models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(1), pages 125-150, January.
    21. Bruce E. Hansen & Seojeong Lee, 2021. "Inference for Iterated GMM Under Misspecification," Econometrica, Econometric Society, vol. 89(3), pages 1419-1447, May.
    22. Li, Lianyou & Song, Ze & Ma, Chao, 2015. "Engel curves and price elasticity in urban Chinese Households," Economic Modelling, Elsevier, vol. 44(C), pages 236-242.
    23. Dias, Gustavo Fruet, 2017. "The time-varying GARCH-in-mean model," Economics Letters, Elsevier, vol. 157(C), pages 129-132.
    24. 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.
    25. De Blander, Rembert, 2020. "Iterative estimation correcting for error auto-correlation in short panels, applied to lagged dependent variable models," Econometrics and Statistics, Elsevier, vol. 15(C), pages 3-29.

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