Outlier robust small domain estimation via bias correction and robust bootstrapping

Bertarelli, Gaia; Chambers, Ray; Salvati, Nicola

doi:10.1007/s10260-020-00514-w

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…Later researches on robust SAE are completed on the basis of the above research. Such as, robust SAE in business surveys is discussed by using robust projection and M-quantile method in [22,23] studied the robust estimation of nested error linear regression model by using huber's ϕ-function and M-quantile based on hierarchical bayes theory and given prior information; The robust SAE of generalized linear models is discussed in [24,25] reviewed the robust estimation of small area with outliers, and proposed Bootstrap MSE based on M-quantile estimators. [26] provide an overview of robust small area estimation.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

“…[26] provide an overview of robust small area estimation. Readers who are interested in this research can refer to [22][23][24][25][26][27]. In this paper, we propose a new robust Bayes estimator using dendity power divergence, and investigate the proposed estimator's MSE and parameter estimation.…”

Section: Introductionmentioning

confidence: 99%