Additive partially linear models for massive heterogeneous data
Document Type
Article
Publication Date
1-1-2019
Abstract
We consider an additive partially linear framework for modelling massive heterogeneous data. The major goal is to extract multiple common features simultaneously across all sub-populations while exploring heterogeneity of each sub-population. We propose an aggregation type of estimators for the commonality parameters that possess the asymptotic optimal bounds and the asymptotic distributions as if there were no heterogeneity. This oracle result holds when the number of sub-populations does not grow too fast and the tuning parameters are selected carefully. A plug-in estimator for the heterogeneity parameter is further constructed, and shown to possess the asymptotic distribution as if the commonality information were available. Furthermore, we develop a heterogeneity test for the linear components and a homogeneity test for the non-linear components accordingly. The performance of the proposed methods is evaluated via simulation studies and an application to the Medicare Provider Utilization and Payment data.
Identifier
85062402621 (Scopus)
Publication Title
Electronic Journal of Statistics
External Full Text Location
https://doi.org/10.1214/18-EJS1528
ISSN
19357524
First Page
391
Last Page
431
Issue
1
Volume
13
Recommended Citation
Wang, Binhuan; Fang, Yixin; Lian, Heng; and Liang, Hua, "Additive partially linear models for massive heterogeneous data" (2019). Faculty Publications. 8082.
https://digitalcommons.njit.edu/fac_pubs/8082