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Small area quantile estimation via spline regression and empirical likelihood

机译：通过样条回归和经验似的小区定量估计

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This paper studies small area quantile estimation under a unit level non-parametric nested-error regression model. We assume the small area specific error distributions satisfy a semi-parametric density ratio model. We fit the non-parametric model via the penalized spline regression method of Opsomer, Claeskens, Ranalli, Kauermann and Breidt (2008). Empirical likelihood is then applied to estimate the parameters in the density ratio model based on the residuals. This leads to natural area-specific estimates of error distributions. A kernel method is then applied to obtain smoothed error distribution estimates. These estimates are then used for quantile estimation in two situations: one is where we only have knowledge of covariate power means at the population level, the other is where we have covariate values of all sample units in the population. Simulation experiments indicate that the proposed methods for small area quantiles estimation work well for quantiles around the median in the first situation, and for a broad range of the quantiles in the second situation. A bootstrap mean square error estimator of the proposed estimators is also investigated. An empirical example based on Canadian income data is included.
机译：本文在单位级非参数嵌套误差回归模型下研究了小面积分位数估计。我们假设小面积特定的误差分布满足半参数密度比模型。我们通过Opsomer，Claeskens，Ranalli，Kauermann和Breidt（2008）的惩罚样条回归方法符合非参数模型。然后应用经验似然来估计基于残差的密度比模型中的参数。这导致自然区域特定的误差分布估计。然后应用内核方法以获得平滑的误差分布估计。然后将这些估计用于两种情况下的定量估计：一个是我们只有在人口层面的协变量手段知识，另一个是我们在人口中所有样本单元的协会值。仿真实验表明，在第一局势中，用于中位数的大面积估计的估计方法很好，以及在第二种情况下广泛的量级。还调查了拟议估算器的自举平均误差估计。包括基于加拿大收入数据的实证例子。

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