Electronic Journal of Statistics

On inference validity of weighted U-statistics under data heterogeneity

Fang Han and Tianchen Qian

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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.

Article information

Electron. J. Statist., Volume 12, Number 2 (2018), 2637-2708.

Received: August 2017
First available in Project Euclid: 31 August 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62E20: Asymptotic distribution theory

Weighted U-statistics nondegeneracy bootstrap inference data heterogeneity rank correlation average-precision correlation

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Han, Fang; Qian, Tianchen. On inference validity of weighted U-statistics under data heterogeneity. Electron. J. Statist. 12 (2018), no. 2, 2637--2708. doi:10.1214/18-EJS1462. https://projecteuclid.org/euclid.ejs/1535681029

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