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Moment convergence of M‐estimators

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  • Yoichi Nishiyama

Abstract

This study extends the rate of convergence theorem of M‐estimators presented by van der Vaart and Wellner (weak convergence and empirical processes: with applications to statistics, Springer‐Verlag, Newyork, 1996) who gave a result of the form r to a result of the form supnE | r , for any p≥1. This result is useful for deriving the moment convergence of the rescaled residual. An application to maximum likelihood estimators is discussed.

Suggested Citation

  • Yoichi Nishiyama, 2010. "Moment convergence of M‐estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(4), pages 505-507, November.
    • Handle: RePEc:bla:stanee:v:64:y:2010:i:4:p:505-507
    DOI: 10.1111/j.1467-9574.2010.00469.x
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    Cited by:

    1. Kato Kengo, 2011. "A note on moment convergence of bootstrap M-estimators," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 51-61, March.
    2. Guang Cheng, 2015. "Moment Consistency of the Exchangeably Weighted Bootstrap for Semiparametric M-estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 665-684, September.

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