ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 1503.04161
92
10
v1v2 (latest)

Studentized sequential U-quantiles under dependence with applications to change-point analysis

13 March 2015
D. Vogel
Martin Wendler
ArXiv (abs)PDFHTML
Abstract

Many popular robust estimators are UUU-quantiles, most notably the Hodges-Lehmann location estimator and the QnQ_nQn​ scale estimator. We prove a functional central limit theorem for the sequential UUU-quantile process without any moment assumptions and under weak short-range dependence conditions. We further devise an estimator for the long-run variance and show its consistency, from which the convergence of the studentized version of the sequential UUU-quantile process to a standard Brownian motion follows. This result can be used to construct CUSUM-type change-point tests based on UUU-quantiles, which do not rely on bootstrapping procedures. We demonstrate this approach in detail at the example of the Hodges-Lehmann estimator for robustly detecting changes in the central location. A simulation study confirms the very good robustness and efficiency properties of the test. Two real-life data sets are analyzed.

View on arXiv
Comments on this paper