A Moment-assisted Approach for Improving Subsampling-based MLE with Large-scale data

TL;DR

This paper introduces a moment-assisted subsampling method to enhance the efficiency of maximum likelihood estimation on large datasets, reducing computational costs while maintaining accuracy.

Contribution

The paper proposes a novel moment-assisted subsampling approach that incorporates sample moments to improve efficiency of MLE with large-scale data.

Findings

MAS estimator has smaller asymptotic variance than traditional subsampling estimators.

The optimal moment minimizes the asymptotic variance, matching full data estimator efficiency.

Numerical results show improved estimation accuracy and computational speed.

Abstract

The maximum likelihood estimation is computationally demanding for large datasets, particularly when the likelihood function includes integrals. Subsampling can reduce the computational burden, but it often results in efficiency loss.This paper proposes a moment-assisted subsampling (MAS) method that can improve the estimation efficiency of existing subsampling-based maximum likelihood estimators.The motivation behind this approach stems from the fact that sample moments can be efficiently computed even if the sample size of the whole data set is huge.Through the generalized method of moments, the proposed method incorporates informative sample moments of the whole data. The MAS estimator can be computed rapidly and is asymptotically normal with a smaller asymptotic variance than the corresponding estimator without incorporating sample moments of the whole data. The asymptotic variance of the proposed estimator depends on the specific sample moments incorporated. We derive the optimal moment that minimizes the resulting asymptotic variance in terms of Loewner order. The proposed MAS estimator can achieve the same estimation efficiency as the whole data-based estimator when the optimal moment is incorporated. Numerical results demonstrate the promising performance of the proposed method in both estimation and computational efficiency compared with existing subsampling methods.