A PARTIALLY LINEAR FRAMEWORK FOR MASSIVE HETEROGENEOUS DATA

We consider a partially linear framework for modelling massive heterogeneous data. The major goal is to extract common features across all sub-populations while exploring heterogeneity of each sub-population. In particular, we propose an aggregation type estimator for the commonality parameter that...

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Vydáno v:The Annals of statistics Ročník 44; číslo 4; s. 1400
Hlavní autoři: Zhao, Tianqi, Cheng, Guang, Liu, Han
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States 01.08.2016
Témata:
partially linear model
joint asymptotics
heterogenous data
massive data
mean square error
reproducing kernel Hilbert space
bias propagation
ISSN:0090-5364
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Shrnutí:We consider a partially linear framework for modelling massive heterogeneous data. The major goal is to extract common features across all sub-populations while exploring heterogeneity of each sub-population. In particular, we propose an aggregation type estimator for the commonality parameter that possesses the (non-asymptotic) minimax optimal bound and asymptotic distribution as if there were no heterogeneity. This oracular result holds when the number of sub-populations does not grow too fast. 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. We also test the heterogeneity among a large number of sub-populations. All the above results require to regularize each sub-estimation as though it had the entire sample size. Our general theory applies to the divide-and-conquer approach that is often used to deal with massive homogeneous data. A technical by-product of this paper is the statistical inferences for the general kernel ridge regression. Thorough numerical results are also provided to back up our theory.
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ISSN:0090-5364
DOI:10.1214/15-AOS1410