The Annals of Statistics

Global testing against sparse alternatives in time-frequency analysis

T. Tony Cai, Yonina C. Eldar, and Xiaodong Li

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Abstract

In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit minimax detection boundary is established between the rareness and weakness of the complex sinusoids hidden in the series. The OPHC test is shown to be asymptotically powerful in the detectable region. Numerical simulations illustrate and verify the effectiveness of the proposed test. Furthermore, the periodogram over-sampled by $O(\log N)$ is proven universally optimal in global testing for periodicities under a mild minimum separation condition.

Article information

Source
Ann. Statist., Volume 44, Number 4 (2016), 1438-1466.

Dates
Received: June 2015
Revised: October 2015
First available in Project Euclid: 7 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.aos/1467894704

Digital Object Identifier
doi:10.1214/15-AOS1412

Mathematical Reviews number (MathSciNet)
MR3519929

Zentralblatt MATH identifier
1359.62032

Subjects
Primary: 62C20: Minimax procedures 62F03: Hypothesis testing 62F05: Asymptotic properties of tests 62G30: Order statistics; empirical distribution functions 62G32: Statistics of extreme values; tail inference

Keywords
Testing for periodicity sparsity over-sampled periodogram higher criticism detection boundary empirical processes

Citation

Cai, T. Tony; Eldar, Yonina C.; Li, Xiaodong. Global testing against sparse alternatives in time-frequency analysis. Ann. Statist. 44 (2016), no. 4, 1438--1466. doi:10.1214/15-AOS1412. https://projecteuclid.org/euclid.aos/1467894704


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