Efficient distributed estimation for expectile regression in increasing dimensions

Abstract

In this paper, we introduce an efficient surrogate loss method for large-scale expectile regression in non-randomly distributed scenarios. Specifically, a Poisson subsampling-based distributed asymmetric least squares estimator is proposed. Our theoretical analysis establishes the consistency and asymptotic normality as the dimensionality tends to infinity, demonstrating that the proposed estimator achieves statistical efficiency comparable to that of the global estimator. A practical three-step algorithm is presented, offering an efficient implementation in practical applications. The proposed estimator exhibits two notable advantages: (i) it is communication-efficient, utilising all the data but only requiring the transmission of a small subsample and the local gradient from each local site; and (ii) it can effectively adapt to unevenly distributed data and non-randomly stored data. Within the Newton-Raphson algorithm, the initial value and the Hessian matrix are computed with enhanced robustness using the Poisson subsampling-derived subsample than using one local dataset or uniform subsampling-derived subsample. Both simulation studies and empirical results confirm that the proposed estimator enhanced estimation efficiency relative to existing methods.