We introduce a sparse estimation in the ordinary kriging for functional data. The functional kriging predicts a feature given as a function at a location where the data are not observed by a linear combination of data observed at other locations. To estimate the weights of the linear combination, we apply the lasso-type regularization in minimizing the expected squared error. We derive an algorithm to derive the estimator using the augmented Lagrange method. Tuning parameters included in the estimation procedure are selected by cross-validation. Since the proposed method can shrink some of the weights of the linear combination toward zeros exactly, we can investigate which locations are necessary or unnecessary to predict the feature. Simulation and real data analysis show that the proposed method appropriately provides reasonable results.

翻译：本文提出了函数型数据普通克里金中的稀疏估计方法。函数克里金通过其他位置观测数据的线性组合，预测未观测位置的特征函数。通过最小化期望平方误差，我们引入套索型正则化来估计线性组合的权重。利用增广拉格朗日方法推导出估计量的求解算法，并通过交叉验证选择估计过程中的调优参数。由于所提方法能将部分线性组合权重精确收缩至零，我们能够识别对预测特征必要或不必要的观测位置。仿真实验与真实数据分析表明，所提方法能合理给出有效结果。