A massive data framework for M-estimators with cubic-rate

Shi, Chengchun, Lu, Wenbin and Song, Rui (2018) A massive data framework for M-estimators with cubic-rate. Journal of the American Statistical Association, 113 (524). 1698 - 1709. ISSN 0162-1459

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Abstract

The divide and conquer method is a common strategy for handling massive data. In this article, we study the divide and conquer method for cubic-rate estimators under the massive data framework. We develop a general theory for establishing the asymptotic distribution of the aggregated M-estimators using a weighted average with weights depending on the subgroup sample sizes. Under certain condition on the growing rate of the number of subgroups, the resulting aggregated estimators are shown to have faster convergence rate and asymptotic normal distribution, which are more tractable in both computation and inference than the original M-estimators based on pooled data. Our theory applies to a wide class of M-estimators with cube root convergence rate, including the location estimator, maximum score estimator, and value search estimator. Empirical performance via simulations and a real data application also validate our theoretical findings. Supplementary materials for this article are available online.

Item Type:	Article
Official URL:	https://www.tandfonline.com/toc/uasa20/current
Additional Information:	© 2018 American Statistical Association
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	15 Oct 2019 12:30
Last Modified:	16 Apr 2024 18:15
URI:	http://eprints.lse.ac.uk/id/eprint/102111

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