Mean estimation with data missing at random for functional covariables
Mean estimation with data missing at random for functional covariables
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DOI：
10.1080/02331888.2011.650172
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发表时间：
2013-08-01
期刊：
影响因子：
1.9
通讯作者：
Vieu, Philippe
中科院分区：
文献类型：
--
作者：
Ferraty, Frederic;Sued, Mariela;Vieu, Philippe
在缺失数据的情况下，我们希望估计标量结果的均值，基于样本，其中每个受试者都观察到一个解释变量，而其中一些受试者的反应偶然缺失。当解释变量为泛函时，我们考虑均值响应的两种估计。一种是基于预测值的平均值，第二种是Horvitz-Thompson估计器的功能适应。我们表明，无穷维的问题并不影响收敛速度的估计是根-n一致的，在随机缺失（MAR）的假设。这些渐近功能完成的模拟实验，说明易于实施和有限的样本量的方法的良好行为。这是第一篇论文强调，平均估计，众所周知的多元非参数统计的不敏感性，仍然是真实的无穷维协变量。从这个意义上说，这项工作开辟了各种其他结果的功能数据分析。
In a missing-data setting, we want to estimate the mean of a scalar outcome, based on a sample in which an explanatory variable is observed for every subject while responses are missing by happenstance for some of them. We consider two kinds of estimates of the mean response when the explanatory variable is functional. One is based on the average of the predicted values and the second one is a functional adaptation of the Horvitz-Thompson estimator. We show that the infinite dimensionality of the problem does not affect the rates of convergence by stating that the estimates are root-n consistent, under missing at random (MAR) assumption. These asymptotic features are completed by simulated experiments illustrating the easiness of implementation and the good behaviour on finite sample sizes of the method. This is the first paper emphasizing that the insensitiveness of averaged estimates, well known in multivariate non-parametric statistics, remains true for an infinite-dimensional covariable. In this sense, this work opens the way for various other results of this kind in functional data analysis.