Using Complex Surveys to Estimate the L1-Median of a Functional Variable: Application to Electricity Load Curves
Using Complex Surveys to Estimate the L1-Median of a Functional Variable: Application to Electricity Load Curves
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DOI：
10.1111/j.1751-5823.2011.00172.x
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发表时间：
2012-04-01
影响因子：
2
通讯作者：
Goga, Camelia
中科院分区：
文献类型：
--
作者：
Chaouch, Mohamed;Goga, Camelia
平均配置文件被广泛用作客户用电习惯的指标。目前，在法国电力公司(EDF)，等级负荷分布是使用逐点平均分布来估计的。不幸的是，众所周知，均值对异常值的存在高度敏感，例如一个或多个消费水平异常高的消费者。在本文中，我们提出了一种替代平均轮廓的方法：L-1-中值轮廓，它更稳健。在处理功能数据(例如负荷曲线)的大数据集时，调查抽样方法对于估计中位数分布是有用的，而不必存储整个数据。这里我们提出了几种抽样策略和估计器来估计中值轨迹。通过测试总体说明了它们之间的比较。我们发展了一种基于线性化变量的分层，与没有替换的简单随机抽样相比，该分层大大提高了估计器的精度。我们还建议了一种考虑辅助信息的改进估计器。文中还强调了未来研究的一些潜在领域。
Mean profiles are widely used as indicators of the electricity consumption habits of customers. Currently, in Electricite De France (EDF), class load profiles are estimated using point-wise mean profiles. Unfortunately, it is well known that the mean is highly sensitive to the presence of outliers, such as one or more consumers with unusually high-levels of consumption. In this paper, we propose an alternative to the mean profile: the L-1-median profile which is more robust. When dealing with large data sets of functional data (load curves for example), survey sampling approaches are useful for estimating the median profile avoiding storing the whole data. We propose here several sampling strategies and estimators to estimate the median trajectory. A comparison between them is illustrated by means of a test population. We develop a stratification based on the linearized variable which substantially improves the accuracy of the estimator compared to simple random sampling without replacement. We suggest also an improved estimator that takes into account auxiliary information. Some potential areas for future research are also highlighted.