On Almost Sure Expansions for $M$-Estimates

Carroll, Raymond J.

doi:10.1214/aos/1176344126

Cited by 49 publications

(15 citation statements)

References 8 publications

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“…In the literature, a number of different Bahadur representations have been obtained under various different settings. Carroll (1978) and Martinsek (1989) obtained strong representations for location and regression M-estimators with preliminary scale estimates, while Babu (1989) and Pollard (1991) obtained the Bahadur representation for the least absolute deviation regression. In addition, Portnoy (1997) obtained the Bahadur representation for quantile smoothing splines, while Portnoy (2003) did so for the censored quantile of the Cox model.…”

Section: Introductionmentioning

confidence: 99%

Uniform Bahadur Representation for Nonparametric Censored Quantile Regression: A Redistribution-of-Mass Approach

Kong

Xia

2016

Econom. Theory

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Abstract. Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of "redistribution-of-mass" (Efron, 1967) has better numerical performance than other available methods. In this paper, this idea is combined with the local polynomial kernel smoothing for nonparametric quantile regression of censored data. We derive the uniform Bahadur representation for the estimator and, more importantly, give theoretical justification for its improved efficiency over existing estimation methods. We include an example to illustrate the usefulness of such a uniform representation in the context of sufficient dimension reduction in regression analysis. Finally, simulations are used to investigate the finite sample performance of the new estimator.

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Section: Introductionmentioning

confidence: 99%

Uniform Bahadur Representation for Nonparametric Censored Quantile Regression: A Redistribution-of-Mass Approach

Kong

Xia

2016

Econom. Theory

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“…If one relaxes the assumption on symmetric or elliptical distributions, the calculation of the asymptotic distribution of robust estimators becomes involved (for example, for the linear regression case see Carroll 1978Carroll , 1979Huber 1981;Rocke and Downs 1981;Carroll and Welsh 1988;Salibian-Barrera 2000;Croux et al 2003). …”

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confidence: 99%

Fast and robust bootstrap

Salibián‐Barrera

Aelst

Willems

2007

Stat. Meth. & Appl.

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“…In statistics, classical work centers around the Bahadur representations for sample quantiles; see Kiefer [18] for a bibliography. For one-dimensional M-estimators of location (with a preliminary estimate of the scale), a strong invariance principle was obtained by Carroll [3]. Related results also appear in Jurecková and Sen [17] and Sen [24].…”

Section: Introductionmentioning

confidence: 66%