Horvitz-Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling
函数型数据的 Horvitz–Thompson 估计：渐近置信带与分层抽样最优配置
When dealing with very large datasets of functional data, survey sampling approaches are useful in order to obtain estimators of simple functional quantities, without being obliged to store all the data. We propose a Horvitz–Thompson estimator of the mean trajectory. In the context of a superpopulation framework, we prove, under mild regularity conditions, that we obtain uniformly consistent estimators of the mean function and of its variance function. With additional…