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Asymptotics of generalized M-estimation of regression and scale with fixed carriers, in an approximately linear model

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  • Wiens, Douglas P.

Abstract

For the approximately linear model , with i.i.d. errors [epsilon]i and fixed carriers z(xi), we establish the asymptotic normality of a generalized M-estimator of regression/scale. The estimator minimizes a weighted Huber-Dutter loss function. The function fn(x) contributes a bias term to the asymptotic normal distribution; apart from this term the estimator is [radical sign]n-equivalent to the estimator obtained assuming the response to be exactly linear. Several estimate/design combinations are compared, in a simulation study.

Suggested Citation

  • Wiens, Douglas P., 1996. "Asymptotics of generalized M-estimation of regression and scale with fixed carriers, in an approximately linear model," Statistics & Probability Letters, Elsevier, vol. 30(3), pages 271-285, October.
    • Handle: RePEc:eee:stapro:v:30:y:1996:i:3:p:271-285
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    Cited by:

    1. Du, Zhiyi & Wiens, Douglas P., 2000. "Jackknifing, weighting, diagnostics and variance estimation in generalized M-estimation," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 287-299, February.
    2. Wiens, Douglas P. & Wu, Eden K.H., 2010. "A comparative study of robust designs for M-estimated regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1683-1695, June.

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