Abstract

The random weighting (RW) approach, recognized as a flexible alternative to

the classical bootstrap method, has been widely employed for approximating the

distribution of parameter estimates. Nevertheless, existing theoretical results for

the RW approach primarily address scenarios where the parameter dimension

remains fixed.

In this paper, we investigate the RW method of M-estimators

under general parametric models with increasing dimensions. We establish that

the RW estimator has the same asymptotic distribution as that of the parameter M-estimate, which suggests that statistical inference regarding the parameter

M-estimate can proceed without estimating nuisance parameters involved in its

asymptotic distribution. Statistical properties of the RW estimator, such as the

Bahadur representation and convergence rate, are also established. Furthermore,

we illustrate the applicability of our theoretical findings through several concrete

models, including linear regression, logistic regression, and spatial median estimation for multivariate data. Simulation studies and real data analysis demonstrate

the superior performance of the proposed RW method.

Information

Preprint No.SS-2025-0132
Manuscript IDSS-2025-0132
Complete AuthorsRuixing Ming, Chengyao Yu, Min Xiao, Zhanfeng Wang
Corresponding AuthorsZhanfeng Wang
Emailszfw@ustc.edu.cn

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Acknowledgments

This work was supported by the Characteristic & Preponderant Discipline

of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang

University-Statistics) and the Collaborative Innovation Center of Statistical Data Engineering Technology & Application, and the National Science

Foundation of China (No. 12371277, No. 12231017).

Supplementary Materials

The supplementary material contains the proofs of all theorems, propositions, and corollaries, as well as the details of the simulations.

Supplementary materials are available for download.