2011
DOI: 10.1198/jasa.2011.tm09774
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Projection Estimators for Generalized Linear Models

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Cited by 24 publications
(18 citation statements)
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“…We simulated the following estimators: the maximum likelihood estimator (ML), the robust quasi likelihood estimators proposed by Cantoni and Ronchetti (2001) with no weights (QL) and with weights (WQL), the conditionally unbiased bounded influence estimator (CUBIF) proposed by Künsch et al (1989), the one step M-estimator starting from the projection estimate (PM) proposed in Bergesio and Yohai (2011) and the MT-and WMT-estimators proposed here. The MT-and the WMT-estimators were computed using a function ρ in the family given in (13).…”
Section: Monte Carlo Studymentioning
confidence: 99%
See 1 more Smart Citation
“…We simulated the following estimators: the maximum likelihood estimator (ML), the robust quasi likelihood estimators proposed by Cantoni and Ronchetti (2001) with no weights (QL) and with weights (WQL), the conditionally unbiased bounded influence estimator (CUBIF) proposed by Künsch et al (1989), the one step M-estimator starting from the projection estimate (PM) proposed in Bergesio and Yohai (2011) and the MT-and WMT-estimators proposed here. The MT-and the WMT-estimators were computed using a function ρ in the family given in (13).…”
Section: Monte Carlo Studymentioning
confidence: 99%
“…Therefore the corresponding score function, the sign function, is monotone too. Bergesio and Yohai (2011) introduced projection estimators for GLM which are highly robust but their computation requires algorithms of high complexity. Since these estimators are not asymptotically normal, they propose one-step M-estimators starting at the P-estimator.…”
Section: Introductionmentioning
confidence: 99%
“…Kordzakhia et al [14] introduced a robust logistic regression by minimizing the mean-squared deviance for the worst case contamination. Bergesio and Yohai [15] introduced projection estimators for generalized linear model. These estimators have the same asymptotic normal distribution as the M-estimators.…”
Section: Introductionmentioning
confidence: 99%
“…В работе автора [10] изучается асимптотическое поведение одношаговых M-оценок общего вида (функции, определяющие эти оценки, не связаны со специальной статистической задачей). Терминология одношаговых взвешенных M-оценок и взвешенных M-оценок использовалась, например, в [22] для схожих статистик в специальной обобщенной модели линейной регрессии, а также частично в [2] для одной частной регрессионной задачи.…”
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“…Подчеркнем, что во всех примерах §3 оценки θ * n имеют структуру (21). Отметим еще, что для справедливости центрального условия (22) достаточно, чтобы выполнялись соотношения…”
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