## Electronic Journal of Statistics

### On inference validity of weighted U-statistics under data heterogeneity

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 31 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1535681029

Digital Object Identifier
doi:10.1214/18-EJS1462

Subjects
Primary: 62E20: Asymptotic distribution theory

#### Citation

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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