Robust location estimation with missing data
Robust location estimation with missing data
复制标题
缺失数据的稳健位置估计
DOI：
10.1002/cjs.11163
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
V. Yohai
中科院分区：
文献类型：
--
作者：
M. Sued;V. Yohai
在缺失数据设置中，我们有一个样本，其中对每个受试者i观察到解释变量向量${\bfx}_i$，而标量响应$y_i$因某些个体的偶然性而缺失。在这项工作中，我们提出了在半参数回归模型下，假设随机缺失(MAR)数据的响应分布的稳健估计。我们的方法允许对响应分布的任何弱连续泛函进行一致估计。特别地，给出了任意连续位置泛函，如中值泛函、L泛函和M泛函的强相合估计。对回归模型的稳健拟合与位置泛函的稳健特性相结合，产生了用于估计位置参数的稳健配方。健壮性是通过所提出的程序的故障点来量化的。给出了位置估计器的渐近分布。这些定理的证明在网上可获得的补充材料中给出。《加拿大统计杂志》41：111-132；2013-2012加拿大统计学会
In a missing data setting, we have a sample in which a vector of explanatory variables ${\bf x}_i$ is observed for every subject i, while scalar responses $y_i$ are missing by happenstance on some individuals. In this work we propose robust estimators of the distribution of the responses assuming missing at random (MAR) data, under a semiparametric regression model. Our approach allows the consistent estimation of any weakly continuous functional of the response's distribution. In particular, strongly consistent estimators of any continuous location functional, such as the median, L‐functionals and M‐functionals, are proposed. A robust fit for the regression model combined with the robust properties of the location functional gives rise to a robust recipe for estimating the location parameter. Robustness is quantified through the breakdown point of the proposed procedure. The asymptotic distribution of the location estimators is also derived. The proofs of the theorems are presented in Supplementary Material available online. The Canadian Journal of Statistics 41: 111–132; 2013 © 2012 Statistical Society of Canada