Rendering parametric procedures more robust by empirically tilting the model

Choi, Edwin; Hall, Peter; Presnell, Brett

doi:10.1093/biomet/87.2.453

Cited by 23 publications

(11 citation statements)

References 15 publications

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“…Whereas for γ = 0 the method is known as exponential tilting as defined in Kitamura and Stutzer (1997), Imbens, Spady, and Johnson, (1998), and Newey and Smith (2004). For a given γ, Choi, Hall, and Presnell (2000) considered contamination neighborhoods as discrete distributions within a fixed Cressie-Read divergence neighborhood of the empirical distribution. Optimization over this class of discrete distributions gives a robust estimator whose tradeoff between efficiency and robustness is governed by the size of the neighborhood.…”

Section: Formulation Of the Estimatormentioning

confidence: 99%

Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood

Bondell¹,

Stefanski²

2013

Journal of the American Statistical Association

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Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we develop and study a linear regression estimator that comes close. Efficiency obtains from the estimator’s close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated sum of (weighted) squared residuals. We prove maximum attainable finite-sample replacement breakdown point, and full asymptotic efficiency for normal errors. Simulation evidence shows that compared to existing robust regression estimators, the new estimator has relatively high efficiency for small sample sizes, and comparable outlier resistance. The estimator is further illustrated and compared to existing methods via application to a real data set with purported outliers.

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Section: Formulation Of the Estimatormentioning

confidence: 99%

Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood

Bondell¹,

Stefanski²

2013

Journal of the American Statistical Association

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“…The strategy of setting weights that are proportional to a power transformation of the assumed density has some connections with the methods proposed by Windham [33], Basu et al [6] and Choi, Hall and Presnell [8]. In these approaches, however, the main objective is robust estimation and the weights are set based on a fixed constant not depending on the sample size.…”

mentioning

confidence: 99%

Maximum Lq-likelihood estimation

Ferrari¹,

Yang²

2010

Ann. Statist.

104

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In this paper, the maximum Lq-likelihood estimator (MLqE), a new parameter estimator based on nonextensive entropy [Kibernetika 3 (1967) 30-35] is introduced. The properties of the MLqE are studied via asymptotic analysis and computer simulations. The behavior of the MLqE is characterized by the degree of distortion q applied to the assumed model. When q is properly chosen for small and moderate sample sizes, the MLqE can successfully trade bias for precision, resulting in a substantial reduction of the mean squared error. When the sample size is large and q tends to 1, a necessary and sufficient condition to ensure a proper asymptotic normality and efficiency of MLqE is established.

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“…We mention that Peter also made very influential contributions to the somewhat related area of likelihood tilting, see e.g. Choi et al (2000).…”

Section: Introductionmentioning

confidence: 99%

Hybrid combinations of parametric and empirical likelihoods

Hjort¹,

McKeague²,

Keilegom³

2018

STAT SINICA

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Some personal reflections on PeterWe are all grateful to Peter for his deeply influential contributions to the field of statistics, in particular to the areas of nonparametric smoothing, bootstrap, empirical likelihood (what this paper is about), functional data, high-dimensional data, measurement errors, etc., many of which were major breakthroughs in the area.His services to the profession were also exemplary and exceptional. It seems that he could simply not say 'no' to the many requests for recommendation letters, thesis reports, editorial duties, departmental reviews, and various other requests for help, and as many of us have experienced, he handled all this with an amazing speed, thoroughness and efficiency. We will also remember Peter as a very warm, gentle and humble person, who was particularly supportive to young people.

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Rendering parametric procedures more robust by empirically tilting the model

Cited by 23 publications

References 15 publications

Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood

Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood

Maximum Lq-likelihood estimation

Hybrid combinations of parametric and empirical likelihoods

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