Properties of higher criticism under strong dependence

TL;DR

This paper investigates how higher criticism performs in signal detection with dependent data, revealing that strong dependence can diminish its effectiveness and suggesting alternative methods for better performance.

Contribution

The study characterizes the behavior of higher criticism under strong dependence and compares its performance to other methods like differences and maximum-based approaches.

Findings

Higher criticism's performance is unaffected by short-range dependence.

Strong dependence causes higher criticism to behave as if data are in large blocks.

Alternative methods outperform higher criticism under strong dependence.

Abstract

The problem of signal detection using sparse, faint information is closely related to a variety of contemporary statistical problems, including the control of false-discovery rate, and classification using very high-dimensional data. Each problem can be solved by conducting a large number of simultaneous hypothesis tests, the properties of which are readily accessed under the assumption of independence. In this paper we address the case of dependent data, in the context of higher criticism methods for signal detection. Short-range dependence has no first-order impact on performance, but the situation changes dramatically under strong dependence. There, although higher criticism can continue to perform well, it can be bettered using methods based on differences of signal values or on the maximum of the data. The relatively inferior performance of higher criticism in such cases can be explained in terms of the fact that, under strong dependence, the higher criticism statistic behaves as though the data were partitioned into very large blocks, with all but a single representative of each block being eliminated from the dataset.