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General M-Estimator Processes and their m out of n Bootstrap with Functional Nuisance Parameters

Author

Listed:
  • Salim Bouzebda

    (Université de technologie de Compiègne)

  • Issam Elhattab

    (Université de technologie de Compiègne
    Hassan II University of Casablanca)

  • Anouar Abdeldjaoued Ferfache

    (Université de technologie de Compiègne)

Abstract

In the present paper, we consider the problem of the estimation of a parameter $$\varvec{\theta }$$ θ , in Banach spaces, maximizing some criterion function which depends on an unknown nuisance parameter h, possibly infinite-dimensional. The classical estimation methods are mainly based on maximizing the corresponding empirical criterion by substituting the nuisance parameter by a nonparametric estimator. We show that the M-estimators converge weakly to maximizers of Gaussian processes under rather general conditions. The conventional bootstrap method fails in general to consistently estimate the limit law. We show that the m out of n bootstrap, in this extended setting, is weakly consistent under conditions similar to those required for weak convergence of the M-estimators. The aim of this paper is therefore to extend the existing theory on the bootstrap of the M-estimators. Examples of applications from the literature are given to illustrate the generality and the usefulness of our results. Finally, we investigate the performance of the methodology for small samples through a short simulation study.

Suggested Citation

  • Salim Bouzebda & Issam Elhattab & Anouar Abdeldjaoued Ferfache, 2022. "General M-Estimator Processes and their m out of n Bootstrap with Functional Nuisance Parameters," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2961-3005, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09965-y
    DOI: 10.1007/s11009-022-09965-y
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    References listed on IDEAS

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    1. Pakes, Ariel & Olley, Steven, 1995. "A limit theorem for a smooth class of semiparametric estimators," Journal of Econometrics, Elsevier, vol. 65(1), pages 295-332, January.
    2. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    3. Bouzebda, Salim & Limnios, Nikolaos, 2013. "On general bootstrap of empirical estimator of a semi-Markov kernel with applications," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 52-62.
    4. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(3), pages 295-313, December.
    5. Ma, Shuangge & Kosorok, Michael R., 2005. "Robust semiparametric M-estimation and the weighted bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 190-217, September.
    6. Kristensen, Dennis & Salanié, Bernard, 2017. "Higher-order properties of approximate estimators," Journal of Econometrics, Elsevier, vol. 198(2), pages 189-208.
    7. Laurent Delsol & Ingrid Van Keilegom, 2020. "Semiparametric M-estimation with non-smooth criterion functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 577-605, April.
    8. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    9. Delsol, Laurent & Escanciano, Juan Carlos & Van Keilegom, Ingrid, 2020. "Semiparametric M-estimation with non-smooth criterion functions," LIDAM Reprints ISBA 2020045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Bose, Arup & Chatterjee, Snigdhansu, 2001. "Generalised bootstrap in non-regular M-estimation problems," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 319-328, December.
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    Cited by:

    1. Bouzebda, Salim & Ferfache, Anouar Abdeldjaoued, 2023. "Asymptotic properties of semiparametric M-estimators with multiple change points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    2. Soukarieh, Inass & Bouzebda, Salim, 2023. "Renewal type bootstrap for increasing degree U-process of a Markov chain," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    3. Inass Soukarieh & Salim Bouzebda, 2022. "Exchangeably Weighted Bootstraps of General Markov U -Process," Mathematics, MDPI, vol. 10(20), pages 1-42, October.

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