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：本文提出了一种用于函数数据普通克里金法的稀疏估计方法。函数克里金法通过在其他观测位置处数据的线性组合，来预测在未观测位置处以函数形式给出的特征。为估计该线性组合的权重，我们在最小化期望平方误差时应用了lasso型正则化。我们推导出一种使用增广拉格朗日法求解估计量的算法。估计过程中包含的调优参数通过交叉验证进行选择。由于所提方法能够将线性组合的部分权重精确收缩至零，我们可以探究哪些位置对于特征预测是必要或不必要的。仿真与真实数据分析表明，所提方法能够恰当地给出合理的结果。