On Selection Criteria for the Tuning Parameter in Robust Divergence

Yonekura, Shouto

doi:10.3390/e23091147

Cited by 12 publications

(2 citation statements)

References 14 publications

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“…For the choice of function f , there is a trade-off between robustness against outliers and model efficiency. Methods for determining the tuning parameters of divergence have been studied [48] [49] [50]. These methods can be used to determine the appropriate function f and the strictly convex function ϕ.…”

Section: Discussionmentioning

confidence: 99%

Unbiased Estimating Equation and Latent Bias Under f-Separable Bregman Distortion Measures

Kobayashi,

Watanabe

2024

IEEE Trans. Inform. Theory

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We discuss unbiased estimating equations in a class of objective functions using a monotonically increasing function f and Bregman divergence. The choice of the function f gives desirable properties, such as robustness against outliers. To obtain unbiased estimating equations, analytically intractable integrals are generally required as bias correction terms. In this study, we clarify the combination of Bregman divergence, statistical model, and function f in which the bias correction term vanishes. Focusing on Mahalanobis and Itakura-Saito distances, we generalize fundamental existing results and characterize a class of distributions of positive reals with a scale parameter, including the gamma distribution as a special case. We also generalized these results to general model classes characterized by one-dimensional Bregman divergence. Furthermore, we discuss the possibility of latent bias minimization when the proportion of outliers is large, which is induced by the extinction of the bias correction term. We conducted numerical experiments to show that the latent bias can approach zero under heavy contamination of outliers or very small inliers.

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Section: Discussionmentioning

confidence: 99%

Unbiased Estimating Equation and Latent Bias Under f-Separable Bregman Distortion Measures

Kobayashi,

Watanabe

2024

IEEE Trans. Inform. Theory

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“…In this paper, we use IWJ algorithm to select the optimal tuning parameters. In similar related work, the parameter selection algorithm based on Hyvarinen score is given in [35]. In further research, this algorithm can be applied to the unit level model proposed in this paper, and the purpose of selecting the optimal tuning parameters can also be achieved.…”

Section: Plos Onementioning

confidence: 99%

Robust small area estimation for unit level model with density power divergence

Niu,

Pang,

Wang

2023

PLoS ONE

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Unit level model is one of the classical models in small area estimation, which plays an important role with unit information data. Empirical Bayesian(EB) estimation, as the optimal estimation under normal assumption, is the most commonly used parameter estimation method in unit level model. However, this kind of method is sensitive to outliers, and EB estimation will lead to considerable inflation of the mean square error(MSE) when there are outliers in the responses yij. In this study, we propose a robust estimation method for the unit-level model with outliers based on the minimum density power divergence. Firstly, by introducing the minimum density power divergence function, we give the estimation equation of the parameters of the unit level model, and obtain the asymptotic distribution of the robust parameters. Considering the existence of tuning parameters in the robust estimator, an optimal parameter selection algorithm is proposed. Secondly, empirical Bayesian predictors of unit and area mean in finite populations are given, and the MSE of the proposed robust estimators of small area means is given by bootstrap method. Finally, we verify the superior performance of our proposed method through simulation data and real data. Through comparison, our proposed method can can solve the outlier situation better.

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Robust inference methods for meta‐analysis involving influential outlying studies

Noma,

Sugasawa,

Furukawa

2024

Statistics in Medicine

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Meta‐analysis is an essential tool to comprehensively synthesize and quantitatively evaluate results of multiple clinical studies in evidence‐based medicine. In many meta‐analyses, the characteristics of some studies might markedly differ from those of the others, and these outlying studies can generate biases and potentially yield misleading results. In this article, we provide effective robust statistical inference methods using generalized likelihoods based on the density power divergence. The robust inference methods are designed to adjust the influences of outliers through the use of modified estimating equations based on a robust criterion, even when multiple and serious influential outliers are present. We provide the robust estimators, statistical tests, and confidence intervals via the generalized likelihoods for the fixed‐effect and random‐effects models of meta‐analysis. We also assess the contribution rates of individual studies to the robust overall estimators that indicate how the influences of outlying studies are adjusted. Through simulations and applications to two recently published systematic reviews, we demonstrate that the overall conclusions and interpretations of meta‐analyses can be markedly changed if the robust inference methods are applied and that only the conventional inference methods might produce misleading evidence. These methods would be recommended to be used at least as a sensitivity analysis method in the practice of meta‐analysis. We have also developed an R package, robustmeta, that implements the robust inference methods.

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On Selection Criteria for the Tuning Parameter in Robust Divergence

Cited by 12 publications

References 14 publications

Unbiased Estimating Equation and Latent Bias Under f-Separable Bregman Distortion Measures

Unbiased Estimating Equation and Latent Bias Under f-Separable Bregman Distortion Measures

Robust small area estimation for unit level model with density power divergence

Robust inference methods for meta‐analysis involving influential outlying studies

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