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Limit Theory for U-Statistics under Clustered and Weakly Dependent Data

Emmanuel Selorm Tsyawo

arXiv 19 Aug 2026 · Econometrics

arXiv:2608.18443 · PDF · Extracted main text

Abstract

This paper develops asymptotic theory and feasible inference for unbounded-kernel order-k U-statistics under clustered sampling and weakly dependent time-series sampling. The analysis first builds the complete order-2 pipeline, moving from clustered data to exact m-dependence and then to near-epoch dependence. The same logic is subsequently extended to general order k greater than or equal to 2. Under clustered sampling, the theory allows arbitrary within-cluster dependence and growing, unbalanced cluster sizes. Under weak dependence, an i.i.d.-based approximating sequence carries the exact-m theory to near-epoch-dependent processes. The common combinatorial device is a vertical rearrangement, which isolates sampling-generic tuples, where the first-order Hoeffding projection is analysed, from collision terms and higher-order degenerate remainders, which are controlled explicitly. Cluster-robust and HAC estimators of the covariance of the first-order projection, needed for feasible inference, are shown to be consistent.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Dehling, Herold and Vogel, Daniel and Wendler, Martin and Wied, Domi… (2017) Testing for Changes in Kendall's Tau0.9568488%
2Sen, Pranab Kumar (1963) On the Properties of $U$-Statistics when the Observations are not Independent. Part One: Estimation of Non-Serial Parameters in…0.84333100%
3Janson, Svante (2023) Asymptotic Normality for $m$-Dependent and Constrained $U$-Statistics, with Applications to Pattern Matching in Random Strings a…0.7373367%
4Davidson, James (1994) Stochastic Limit Theory: An Introduction for Econometricians0.6444250%
5de Jong, Robert M. and Davidson, James (2000) Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices0.6444250%
6Henze, Norbert (2024) Asymptotic Stochastics: An Introduction with a View towards Statistics0.6444250%
7Bhattacharya, Debopam (2007) Inference on Inequality from Household Survey Data0.64422100%
8Darku, Francis Bilson and Konietschke, Frank and Chattopadhyay, Bhar… (2020) Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data0.64422100%
9Fischer, Svenja and Fried, Roland and Wendler, Martin (2016) Multivariate Generalized Linear-Statistics of Short Range Dependent Data0.64422100%
10Fischer, Svenja (2017) Robust Estimation Methods with Application to Flood Statistics0.64422100%

Showing the top 10 of 28 scored citations.