symmetric KK theories. As usual we assume that the classical bubble solutions provide useful approximations to solutions in theories with moduli stabilized by additional fluxes or other objects. Ref. [@Dine:2004uw], for example, found that neutral bubble solutions persist after adding simple stabilizing potentials.

[^3]: The matter Lagrangian is normalized as $-\frac{1}{12}\int d^6x\, \sqrt{-g_6}C^2$.

[^4]: We thank Gary Shiu for bringing these solutions to our attention.


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abstract: 'In this paper, we propose a new statistical inference method for massive data sets, which is very simple and efficient by combining divide-and-conquer method and empirical likelihood. Compared with two popular methods (the bag of little bootstrap and the subsampled double bootstrap), we make full use of data sets, and reduce the computation burden. Extensive numerical studies and real data analysis demonstrate the effectiveness and flexibility of our proposed method. Furthermore, the asymptotic property of our method is derived.'
author:
- '   Xuejun MA [^1]    Shaochen WANG [^2]   Wang ZHOU [^3]'
title: ' **Statistical inference in massive datasets by empirical likelihood** '
---

> [*Keywords*]{}: Bootstrap; divide-and-conquer; hypothesis test; empirical likelihood.

> [*MSC2010 subject classifications*]{}: Primary 62G10; secondary 62G05.

Introduction
============

With the rapid development of science and technologies, massive data can be collected at a large speed, especially in internet and financial fields. It is generally recognized that two major challenges in large-scale learning are estimation and inference due to large amount of computation.

For statistical inference on massive data sets, [@Kleiner2014] proposed the bag of little bootstrap (BLB) to assess the quality of estimators. However, they used only a small number of random subsets, and partial observations from each subset. This implies less efficiency in application. So, [@Sengupta2016] developed the subsampled double bootstrap (SDB) method which no