The Annals of Statistics

Inference of weighted $V$-statistics for nonstationary time series and its applications

Zhou Zhou

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Abstract

We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted $V$-statistics through the angle of Fourier analysis. The established theory for $V$-statistics provides a unified treatment for many important time and spectral domain problems in the analysis of nonstationary time series, ranging from nonparametric estimation to the inference of periodograms and spectral densities.

Article information

Source
Ann. Statist., Volume 42, Number 1 (2014), 87-114.

Dates
First available in Project Euclid: 15 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.aos/1389795746

Digital Object Identifier
doi:10.1214/13-AOS1184

Mathematical Reviews number (MathSciNet)
MR3161462

Zentralblatt MATH identifier
1306.62205

Subjects
Primary: 62E20: Asymptotic distribution theory 60F05: Central limit and other weak theorems

Keywords
$V$-statistics Fourier transform nondegeneracy degeneracy locally stationary time series nonparametric inference spectral analysis

Citation

Zhou, Zhou. Inference of weighted $V$-statistics for nonstationary time series and its applications. Ann. Statist. 42 (2014), no. 1, 87--114. doi:10.1214/13-AOS1184. https://projecteuclid.org/euclid.aos/1389795746


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Supplemental materials

  • Supplementary material: Supplement for “Inference of weighted $V$-statistics for nonstationary time series and its applications”. This supplementary material contains auxiliary lemmas and proofs of Propositions 1, 3, 4 and Corollaries 3, 4 of the paper.