Approximate Asymptotic Distribution of Locally Most Powerful Invariant Test for Independence : Complex Case

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1784-1799
Journal / PublicationIEEE Transactions on Information Theory
Issue number3
Online published14 Feb 2017
Publication statusPublished - Mar 2018


Usually, it is very difficult to determine the exact distribution for a test statistic. In this paper, asymptotic distributions of locally most powerful invariant test for independence of complex Gaussian vectors are developed. In particular, its cumulative distribution function (CDF) under the null hypothesis is approximated by a function of chi-squared CDFs. Moreover, the CDF corresponding to the non-null distribution is expressed in terms of non-central chi-squared CDFs for close hypothesis, and Gaussian CDF as well as its derivatives for far hypothesis. The results turn out to be very accurate in terms of fitting their empirical counterparts. Closed-form expression for the detection threshold is also provided. Numerical results are presented to validate our theoretical findings.

Research Area(s)

  • asymptotic series expansion, chi-squared approximation, Independence test, locally most powerful invariant test, threshold calculation