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On Edgeworth Expansion and Moving Block Bootstrap for StudentizedM-Estimators in Multiple Linear Regression Models

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  • Lahiri, Soumendra Nath

Abstract

This paper considers the multiple linear regression modelYi=xi'[beta]+[var epsilon]i,i=i, ..., n, wherexi's are knownp-1 vectors,[beta]is ap-1 vector of parameters, and[var epsilon]1,[var epsilon]2, ... are stationary, strongly mixing random variables. Let[beta]ndenote anM-estimator of[beta]corresponding to some score function[psi]. Under some conditions on[psi],xi's and[var epsilon]i's, a two-term Edgeworth expansion for Studentized multivariateM-estimator is proved. Furthermore, it is shown that the moving block bootstrap is second-order correct for some suitable bootstrap analog of Studentized[beta]n.

Suggested Citation

  • Lahiri, Soumendra Nath, 1996. "On Edgeworth Expansion and Moving Block Bootstrap for StudentizedM-Estimators in Multiple Linear Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 42-59, January.
    • Handle: RePEc:eee:jmvana:v:56:y:1996:i:1:p:42-59
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    Cited by:

    1. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    2. La Vecchia, Davide & Moor, Alban & Scaillet, Olivier, 2023. "A higher-order correct fast moving-average bootstrap for dependent data," Journal of Econometrics, Elsevier, vol. 235(1), pages 65-81.
    3. Romano, Joseph P. & Wolf, Michael, 2001. "Improved nonparametric confidence intervals in time series regressions," DES - Working Papers. Statistics and Econometrics. WS ws010201, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Yixiao Sun & Peter C.B. Phillips, 2008. "Optimal Bandwidth Choice for Interval Estimation in GMM Regression," Cowles Foundation Discussion Papers 1661, Cowles Foundation for Research in Economics, Yale University.
    5. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
    6. Inoue, Atsushi & Shintani, Mototsugu, 2006. "Bootstrapping GMM estimators for time series," Journal of Econometrics, Elsevier, vol. 133(2), pages 531-555, August.
    7. Amilcar Velez, 2023. "The Local Projection Residual Bootstrap for AR(1) Models," Papers 2309.01889, arXiv.org, revised Feb 2024.
    8. Peter Buhlmann, 2007. "Bootstrap schemes for time series (in Russian)," Quantile, Quantile, issue 3, pages 37-56, September.
    9. Ching-Chuan Tsong, 2009. "Assessing the Accuracy of Event Forecasts," Journal of Economics and Management, College of Business, Feng Chia University, Taiwan, vol. 5(2), pages 219-240, July.
    10. S. N. Lahiri, 2018. "Uncertainty Quantification in Robust Inference for Irregularly Spaced Spatial Data Using Block Bootstrap," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 173-221, December.
    11. Härdle, Wolfgang & Horowitz, Joel L. & Kreiss, Jens-Peter, 2001. "Bootstrap methods for time series," SFB 373 Discussion Papers 2001,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Janis J. Zvingelis, 2000. "On Bootstrap Coverage Probability with Dependent Data," Econometric Society World Congress 2000 Contributed Papers 1231, Econometric Society.
    13. Wolfgang Härdle & Joel Horowitz & Jens‐Peter Kreiss, 2003. "Bootstrap Methods for Time Series," International Statistical Review, International Statistical Institute, vol. 71(2), pages 435-459, August.
    14. Blaskowitz, Oliver & Herwartz, Helmut, 2014. "Testing the value of directional forecasts in the presence of serial correlation," International Journal of Forecasting, Elsevier, vol. 30(1), pages 30-42.

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