Asymptotic covariance estimation by Gaussian random perturbation

Jing Zhou, Wei Lan and Hansheng Wang

Computational Statistics & Data Analysis, 2022, vol. 171, issue C

Abstract: In most cases, the asymptotic covariance matrix of an M-estimator is in a sandwich form. This sandwich form involves calculations of the first and second order derivatives of the loss function, which is intractable if the loss function is complex. To alleviate this problem, we propose in this article a novel method called Gaussian random perturbation. This method can be used to estimate the asymptotic covariance matrix of a general M-estimator without derivative calculations. The idea can be summarized as follows. We first generate a small random perturbation around the M-estimator. Then, we re-evaluate the loss function at the randomly perturbed M-estimator and obtain the estimators of the first and second order derivatives of the loss function via Taylor series expansion. This leads to a novel estimator for the asymptotic covariance matrix. We then rigorously show that the resulting covariance estimator is statistically consistent with two elegant characteristics. First, it involves no computation of derivatives. This makes it easier to estimate the covariance matrix of an M-estimator with a complex loss function. Second, it is convenient for parallel computing and thus attractive for massive data analysis. The consistency of the proposed asymptotic covariance estimator is demonstrated under appropriate regularity conditions. The practical usefulness of the method is further demonstrated with both simulation studies and real data analysis.

Keywords: Covariance matrix estimation; Gaussian random perturbation; M-estimators (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947322000391
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:171:y:2022:i:c:s0167947322000391

DOI: 10.1016/j.csda.2022.107459

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().