Complex Parameter Rao and Wald Tests for Assessing the Bandedness of a Complex-Valued Covariance Matrix
Abstract
:1. Introduction
2. Problem Formulation
3. Methods
3.1. The Complex Rao Test for Testing the Bandedness
3.2. Complex Parameter Wald Test
3.2.1. Complex Wald Test for General Cases
3.2.2. Complex Wald Test for Special Fisher Information Matrix
3.2.3. The Complex Wald Test for Testing Bandedness
4. Simulations, Results and Discussion
4.1. Simulations and Result Discussion on Complex Rao and Wald Tests for Bandedness Testing
4.2. Equivalence among Complex Wald, Rao Test and GlRT for Linear Model
4.2.1. Complex Classical Linear Model Testing Problem
4.2.2. Generalized Likelihood Ratio Test (GlRT)
4.2.3. Complex Rao Test
4.2.4. Complex Wald Test
4.2.5. The Root Cause of the Equivalence
5. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
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Zhu, Z. Complex Parameter Rao and Wald Tests for Assessing the Bandedness of a Complex-Valued Covariance Matrix. Signals 2024, 5, 1-17. https://0-doi-org.brum.beds.ac.uk/10.3390/signals5010001
Zhu Z. Complex Parameter Rao and Wald Tests for Assessing the Bandedness of a Complex-Valued Covariance Matrix. Signals. 2024; 5(1):1-17. https://0-doi-org.brum.beds.ac.uk/10.3390/signals5010001
Chicago/Turabian StyleZhu, Zhenghan. 2024. "Complex Parameter Rao and Wald Tests for Assessing the Bandedness of a Complex-Valued Covariance Matrix" Signals 5, no. 1: 1-17. https://0-doi-org.brum.beds.ac.uk/10.3390/signals5010001