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Sample-based estimation of mean electricity consumption curves for small domains

机译：基于样本的小域平均耗电量曲线估计

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摘要

Many studies conducted by various electric utilities around the world are based on the analysis of mean electricity consumption curves for various subpopulations, particularly geographic in nature. Those mean curves are estimated from samples of thousands of curves measured at very short intervals over long periods. Estimation for small subpopulations, also called small domains, is a very timely topic in sampling theory.In this article, we will examine this problem based on functional data and we will try to estimate the mean curves for small domains. For this, we propose four methods: functional linear regression; modelling the scores of a principal component analysis by unit-level linear mixed models; and two non-parametric estimators, with one based on regression trees and the other on random forests, adapted to the curves. All these methods have been tested and compared using real electricity consumption data for households in France.
机译：全世界各种电力公司进行的许多研究都是基于对各种子种群（尤其是自然地理种群）的平均用电量曲线的分析。这些平均曲线是从很长一段时间内以非常短的时间间隔测得的数千条曲线的样本估算得出的。小样本人口（也称为小域）的估计是抽样理论中非常及时的话题。在本文中，我们将基于功能数据研究此问题，并尝试估计小域的均值曲线。为此，我们提出了四种方法：函数线性回归；通过单元级线性混合模型对主成分分析的分数建模；和两个非参数估计量，其中一个基于回归树，另一个基于随机森林，适用于曲线。使用法国家庭的实际用电量数据对所有这些方法进行了测试和比较。

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