Horvitz--Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling
Horvitz--Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling
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DOI：
10.1093/biomet/asq070
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发表时间：
2009-12
期刊：
影响因子：
2.7
通讯作者：
H. Cardot;E. Josserand
中科院分区：
文献类型：
--
作者：
H. Cardot;E. Josserand
当处理非常大的函数数据集时，调查抽样方法对于获得简单函数量的估计值很有用，而不必存储所有数据。我们提出了平均轨迹的Horvitz—Thompson估计。在超总体框架下，我们证明了在温和正则性条件下，我们得到了均值函数及其方差函数的一致一致估计。通过对抽样设计的附加假设，给出了一个泛函中心极限定理，得到了渐近置信带。对分层抽样进行了详细的研究，并给出了考虑均值方差准则的常用最优分配规则的函数版本。这些技术通过ne18902电表的测试人群来说明，我们在一周内每30分钟对这些电表进行单独的用电量测量。我们表明，与不进行替换的简单随机抽样相比，分层可以大大提高估计器的精度并减小全局置信带的宽度。牛津大学出版社版权所有。
When dealing with very large datasets of functional data, survey sampling approaches are useful in order to obtain estimators of simple functional quantities, without being obliged to store all the data. We propose a Horvitz--Thompson estimator of the mean trajectory. In the context of a superpopulation framework, we prove, under mild regularity conditions, that we obtain uniformly consistent estimators of the mean function and of its variance function. With additional assumptions on the sampling design we state a functional central limit theorem and obtain asymptotic confidence bands. Stratified sampling is studied in detail, and we also obtain a functional version of the usual optimal allocation rule, considering a mean variance criterion. These techniques are illustrated by a test population of Ne18 902 electricity meters for which we have individual electricity consumption measures every 30 minutes over one week. We show that stratification can substantially improve both the accuracy of the estimators and reduce the width of the global confidence bands compared with simple random sampling without replacement. Copyright 2011, Oxford University Press.