Test for a specified signal when the noise covariance matrix is unknown

Khatri, C. G. ; Radhakrishna Rao, C. (1987) Test for a specified signal when the noise covariance matrix is unknown Journal of Multivariate Analysis, 22 (2). pp. 177-188. ISSN 0047-259X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/004725...

Related URL: http://dx.doi.org/10.1016/0047-259X(87)90084-4


In the univariate case it is well known that the one sided t test is uniformly most powerful for the null hypothesis against all one sided alternatives. Such a property does not easily extend to the multivariate case. In this paper, a test derived for the hypothesis that the mean of a vector random variable is zero against specified alternatives, when the covariance matrix is unknown. This test depends on the given alternatives and is more powerful than Hotelling's T2. The results are derived both for real and complex vector observations and under normal and spherical distributions. The properties of the proposed tests are investigated in detail when a single alternative is specified.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Complex Normal; Conditional Tests; Hotelling's T2; Rao's U Statistic; Student's t
ID Code:42466
Deposited On:02 Jun 2011 14:37
Last Modified:02 Jun 2011 14:37

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