2021/04/08 by Hua Liu, Liu, Hua, Jinhong You +3
Computer Science · Engineering · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #stat.CO #stat.ME
paper · pdf · doi:10.48550/arxiv.2104.03446
37 pages and 15 figures
openalex publication_date 2021/04/08 · arxiv created 2021/07/06 · arxiv updated 2021/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Massive data bring the big challenges of memory and computation for analysis. These challenges can be tackled by taking subsamples from the full data as a surrogate. For functional data, it is common to collect multiple measurements over their domains, which require even more memory and computation time when the sample size is large. The computation would be much more intensive when statistical inference is required through bootstrap samples. To the best of our knowledge, this article is the first attempt to study the subsampling method for the functional linear model. We propose an optimal subsampling method based on the functional L-optimality criterion. When the response is a discrete or categorical variable, we further extend our proposed functional L-optimality subsampling (FLoS) method to the functional generalized linear model. We establish the asymptotic properties of the estimators by the FLoS method. The finite sample performance of our proposed FLoS method is investigated by extensive simulation studies. The FLoS method is further demonstrated by analyzing two large-scale datasets: the global climate data and the kidney transplant data. The analysis results on these data show that the FLoS method is much better than the uniform subsampling approach and can well approximate the results based on the full data while dramatically reducing the computation time and memory.