Robust Weighted Likelihood Estimation of Exponential Parameters

Ahmed, Ejaz; Volodin, Andrei; Hussein, Abdulkadir

doi:10.1109/tr.2005.853276

Cited by 36 publications

(15 citation statements)

References 15 publications

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“…This corresponds to a result of Ahmed et al (2005) who showed that the TLE for the exponential distribution behaves asymptotically like a one-sided trimmed mean.…”

Section: Corollarysupporting

confidence: 84%

“…is given by (1). The original h-trimmed likelihood estimator can be obtained by calculating the maximum likelihood estimator θ Z of each subset Z of data points with N − h elements and defining Z 0…”

Section: Definition 2 (See Müller and Neykov 2003)mentioning

confidence: 99%

“…Additionally, Ahmed et al (2005) provide a relative bias and a quadratic risk as robustness measures for trimmed likelihood estimators for the exponential distribution in the case of one stress level. They show in particular that their estimator is asymptotically equivalent with the simple one-sided α-trimmed mean.…”

Section: Introductionmentioning

confidence: 99%

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Trimmed likelihood estimators for lifetime experiments and their influence functions

et al. 2015

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We study the behavior of trimmed likelihood estimators for lifetime models with exponential or lognormal distributions possessing a linear or nonlinear link function. In particular we investigate the difference between two possible definitions for the trimmed likelihood estimator, one called original trimmed likelihood estimator (OTLE) and one called modified trimmed likelihood estimator (MTLE) which is the finite sample version of a form for location and linear regression used by Clarke (1993, 2002) and Bednarski et al. (2010). The OTLE is always a MTLE but the MTLE may not be unique even in cases where the OLTE is unique. We compare especially the functional forms of both types of estimators, characterize the difference with the implicit function theorem and indicate situations where they coincide and where they do not coincide. Since the functional form of the MTLE has a simpler form, we use it then for deriving the influence function, again with the help of the implicit function theorem. The derivation of the influence function for the functional form of the OTLE is similar but more complicated.

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“…This corresponds to a result of Ahmed et al (2005) who showed that the TLE for the exponential distribution behaves asymptotically like a one-sided trimmed mean.…”

Section: Corollarysupporting

confidence: 84%

Section: Definition 2 (See Müller and Neykov 2003)mentioning

confidence: 99%

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Trimmed likelihood estimators for lifetime experiments and their influence functions

et al. 2015

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“…Further, the WMLE basically provides the MLE if we assume that all weights are equal to one. The statistical asymptotic properties of the WMLE have been studied in Wang, Van Eeden, and Zidek (2004) and Ahmed, Volodin, and Hussein (2005).…”

Section: J Almutawamentioning

confidence: 99%

“…To overcome this problem, many robust alternatives of the MLE have been developed in the last decades. One approach is to imitate the weighted least squares estimation and to define the WMLE (Ahmed et al, 2005;Picci & Katayama, 1996;Wang et al, 2004) accordingly; i.e.…”

Section: Maximum Likelihood Estimation With Outliersmentioning

confidence: 99%

Robust maximum likelihood estimation for stochastic state space model with observation outliers

AlMutawa

2015

International Journal of Systems Science

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The objective of this paper is to develop a robust maximum likelihood estimation (MLE) for the stochastic state space model via the expectation maximisation algorithm to cope with observation outliers. Two types of outliers and their influence are studied in this paper: namely,the additive outlier (AO) and innovative outlier (IO). Due to the sensitivity of the MLE to AO and IO, we propose two techniques for robustifying the MLE: the weighted maximum likelihood estimation (WMLE) and the trimmed maximum likelihood estimation (TMLE). The WMLE is easy to implement with weights estimated from the data; however, it is still sensitive to IO and a patch of AO outliers. On the other hand, the TMLE is reduced to a combinatorial optimisation problem and hard to implement but it is efficient to both types of outliers presented here. To overcome the difficulty, we apply the parallel randomised algorithm that has a low computational cost. A Monte Carlo simulation result shows the efficiency of the proposed algorithms.

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Impact on loss/risk assessments of inter-model variability in vulnerability analysis

2013

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Robust Weighted Likelihood Estimation of Exponential Parameters

Cited by 36 publications

References 15 publications

Trimmed likelihood estimators for lifetime experiments and their influence functions

Trimmed likelihood estimators for lifetime experiments and their influence functions

Robust maximum likelihood estimation for stochastic state space model with observation outliers

Impact on loss/risk assessments of inter-model variability in vulnerability analysis

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