Statistics Papers

Document Type

Journal Article

Date of this Version

2016

Publication Source

The Annals of Statistics

Volume

44

Issue

4

Start Page

1438

Last Page

1466

DOI

10.1214/15-AOS1412

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

Copyright/Permission Statement

The original and published work is available at: https://projecteuclid.org/euclid.aos/1467894704

Keywords

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

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Date Posted: 27 November 2017

This document has been peer reviewed.