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基于 M 分位数的小区域估计量的偏差控制AI 解读

Projective outlier-robust M-quantile-based small area estimators can be substantially biased when the sample data contain representative outliers. In this article we propose two new predictive type bias corrected versions of these estimators for continuous and discrete outcomes. Given both area level and individual level outliers in the population, these new estimators are more efficient than the robust-predictive and robust-projective estimators that have been proposed in…

抗异常值的小域估计AI 解读

Summary Recently proposed outlier robust small area estimators can be substantially biased when outliers are drawn from a distribution that has a different mean from that of the rest of the survey data. This naturally leads one to consider an outlier robust bias correction for these estimators. We develop this idea, proposing two different analytical mean-squared error estimators for the ensuing bias-corrected outlier robust estimators. Simulations based on realistic…

用于小区域估计的 M 分位数模型AI 解读

Small area estimation techniques typically rely on regression models that use both covariates and random effects to explain variation between the areas. However, such models also depend on strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow for outlier-robust inference. We describe a new approach to small area estimation that is based on modelling quantilelike parameters of the conditional distribution of…

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M 分位数AI 解读

It is well known that a M-estimator of the centre of symmetry Θ of a symmetric distribution can be defined in terms of either a continuous symmetric loss function ρ or the associated influence functionψ. This estimator is robust if ψ is bounded. In this paper, we develop a generalization of the M-concept to estimation of a quantile analogue of Θ, called a M-quantile, by introducing a particular kind of asymmetry into ψ. A natural consequence is that the M- quantile parameter…