  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.
