The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, a majority of the reconstruction methods rely on estimating the covariance matrix or the components of its eigendecomposition, a task that may be difficult. In particular, the accuracy of the estimation might be affected by the complexity of the covariance function and the poor availability of complete functional data. We introduce a non-parametric alternative based on a novel concept of depth for partially observed functional data. Our simulations point out that the available methods are unbeatable when the covariance function is stationary, and there is a large proportion of complete data. However, our approach was superior when considering non-stationary covariance functions or when the proportion of complete functions is scarce. Moreover, even in the most severe case of having all the functions incomplete, our method performs well meanwhile the competitors are unable. The methodology is illustrated with two real data sets: the Spanish daily temperatures observed in different weather stations and the age-specific mortality by prefectures in Japan.

翻译：文献中广泛审议了从功能抽样中估计缺失的曲线碎片的问题,然而,大多数重建方法都依赖于估计共变矩阵或其异构成分,这项任务可能很困难;特别是,估计的准确性可能受到共变功能复杂性和完整功能数据不足的影响。我们根据对部分观测功能数据的深度的新概念引入了非参数替代方法。我们的模拟指出,当共变功能是固定的,而且完全数据占很大比例时,可用的方法是无法对抗的。然而,在考虑非常变共变功能或完全功能比例不足时,我们的方法优于其他方法。此外,即使最严重的是所有功能不完全,我们的方法在竞争者之间运作良好。这种方法用两种真实的数据集来说明:不同气象站观察到的西班牙日温和日本各省不同年龄的死亡率。