A distributed minimum average variance estimation for sufficient dimension reduction

Minimum average variance estimation (MAVE) is a powerful method to estimate the dimension reduction directions of the central mean subspace. However, when analyzing the Boeing 737 data with more than 600000 samples, the classical MAVE method would suffer from significant computational burden. To address this issue, we introduce a distributed minimum average variance estimation (distMAVE) methodology for sufficient dimension reduction by adopting a distributed computing system. The proposed distMAVE method is able to handle large datasets and make a balance between estimation accuracy and computation efficiency. The asymptotic properties of the distributed estimators are proved, and a practical algorithm is provided for implementation. In addition to the theoretical results, we also demonstrate the effectiveness of the distMAVE method through simulation studies and Boeing 737 dataset.