Screening for Multiple Target Detection

Abstract

We apply statistical selection theory to multiple target detection problems by analyzing the Mahalanobis distances between multivariate normal populations and a desired standard (a known characteristic of a target). We want to achieve the goal of selecting a subset that contains no non target (negative) sites, which entails screening out all non targets. Correct selection (CS) is defined according to this goal. We consider two cases: (1) that all covariance matrices are known; and (2) that all covariance matrices are unknown, including both heteroscedastic and homoscedastic cases. Optimal selection procedures are proposed in order to reach the selection goal. The least favorable configurations (LFC) are found. Tables and figures are presented to illustrate the properties of our proposed procedures. Simulation examples are given to show that our procedures work well. The log-concavity results of the operating characteristic functions are also given.

Keywords:

• Homoscadastic
• Indifferent zone
• Least favorable configuration
• Log-concave
• Non-central Chi-square
• Non-central F
• Positively quadrant dependent
• Preference zone
• Simulation
• Stochastically increasing
• Unimodal

Mathematics Subject Classification:

• Primary 62F07
• Secondary 62P30, 62H10

Acknowledgments

We thank the editor and two referees for careful and patient reading. The referees' helpful and constructive comments and suggestions have significantly improved the presentation of this article