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2018 On inference validity of weighted U-statistics under data heterogeneity
Fang Han, Tianchen Qian
Electron. J. Statist. 12(2): 2637-2708 (2018). DOI: 10.1214/18-EJS1462

Abstract

Motivated by challenges on studying a new correlation measurement being popularized in evaluating online ranking algorithms’ performance, this manuscript explores the validity of uncertainty assessment for weighted U-statistics. Without any commonly adopted assumption, we verify Efron’s bootstrap and a new resampling procedure’s inference validity. Specifically, in its full generality, our theory allows both kernels and weights asymmetric and data points not identically distributed, which are all new issues that historically have not been addressed. For achieving strict generalization, for example, we have to carefully control the order of the “degenerate” term in U-statistics which are no longer degenerate under the empirical measure for non-i.i.d. data. Our result applies to the motivating task, giving the region at which solid statistical inference can be made.

Citation

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Fang Han. Tianchen Qian. "On inference validity of weighted U-statistics under data heterogeneity." Electron. J. Statist. 12 (2) 2637 - 2708, 2018. https://doi.org/10.1214/18-EJS1462

Information

Received: 1 August 2017; Published: 2018
First available in Project Euclid: 31 August 2018

zbMATH: 06942956
MathSciNet: MR3849897
Digital Object Identifier: 10.1214/18-EJS1462

Subjects:
Primary: 62E20

JOURNAL ARTICLE
72 PAGES


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Vol.12 • No. 2 • 2018
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