## The Annals of Statistics

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

Zhou Zhou

#### 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

https://projecteuclid.org/euclid.aos/1389795746

Digital Object Identifier
doi:10.1214/13-AOS1184

Mathematical Reviews number (MathSciNet)
MR3161462

Zentralblatt MATH identifier
1306.62205

#### 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.