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On Bootstrapping M-Estimated Residual Processes in Multiple Linear-Regression Models

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  • Koul, H. L.
  • Lahiri, S. N.

Abstract

It is shown, under fairly general conditions, that Efron's bootstrap procedure captures the limit distribution of weighted empirical processes based on M-estimated residuals in multiple linear regression models. As an application, we construct bootstrap confidence bands for the error distribution function F. The main result can also be used to design distribution-free goodness-of-fit tests for F without any recourse to the split-sample estimation of the regression parameters.

Suggested Citation

  • Koul, H. L. & Lahiri, S. N., 1994. "On Bootstrapping M-Estimated Residual Processes in Multiple Linear-Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 255-265, May.
    • Handle: RePEc:eee:jmvana:v:49:y:1994:i:2:p:255-265
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    Cited by:

    1. Linton, Oliver & Song, Kyungchul & Whang, Yoon-Jae, 2010. "An improved bootstrap test of stochastic dominance," Journal of Econometrics, Elsevier, vol. 154(2), pages 186-202, February.
    2. Holger Dette & Natalie Neumeyer & Ingrid Van Keilegom, 2007. "A new test for the parametric form of the variance function in non‐parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 903-917, November.
    3. Natalie Neumeyer, 2009. "Smooth Residual Bootstrap for Empirical Processes of Non‐parametric Regression Residuals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 204-228, June.
    4. Oliver Linton & Kyungchui (Kevin) Song & Yoon-Jae Whang, 2008. "Bootstrap tests of stochastic dominance with asymptotic similarity on the boundary," CeMMAP working papers CWP08/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Janssen, Paul & Swanepoel, Jan & Veraverbeke, Noël, 2005. "Bootstrapping modified goodness-of-fit statistics with estimated parameters," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 111-121, February.
    6. Mora, Juan & Neumeyer, Natalie, 2005. "The Two-Sample Problem with Regression Errors : An Empirical Process Approach," Technical Reports 2005,05, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Nagel, Eva-Renate & Dette, Holger & Neumeyer, Natalie, 2004. "Bootstrap tests for the error distribution in linear and nonparametric regression models," Technical Reports 2004,38, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    8. Neumeyer, Natalie & Dette, Holger & Nagel, Eva-Renate, 2003. "A note on testing symmetry of the error distribution in linear regression models," Technical Reports 2003,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. Mora, Juan, 2005. "Comparing distribution functions of errors in linear models: A nonparametric approach," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 425-432, July.

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