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Testing for the mean vector of a multivariate normal distribution with a possibly singular dispersion matrix and related results

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  • Bhimasankaram, P.
  • Sengupta, D.

Abstract

Let y [approximate] p ([mu], [Sigma]) where [Sigma], possibly singluar, is unknown. We develop a test for H0: [mu] = [mu]0 against H1:[mu][not equal to][mu]0 based on a random random sample fromy as an extension of Hotelling's T2 test. We show that the same procedure can be used to compute the test statistic in both the cases of the singular and the positive definite dispersion matrices. This development involves the singular Wishart distribution. Motivated by Khatri (1968), we also obtain an expression for the density of the Wishart distribution p(k, [Sigma]) in each o the following cases: (i)[Sigma] positive definite, k

Suggested Citation

  • Bhimasankaram, P. & Sengupta, D., 1991. "Testing for the mean vector of a multivariate normal distribution with a possibly singular dispersion matrix and related results," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 473-478, June.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:6:p:473-478
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    Cited by:

    1. Duchesne, Pierre & Francq, Christian, 2010. "On testing for the mean vector of a multivariate distribution with generalized and {2}-inverses," MPRA Paper 19740, University Library of Munich, Germany.
    2. Osei, Prince P. & Davidov, Ori, 2022. "Bayesian linear models for cardinal paired comparison data," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    3. Arnab Bhattacharjee & Christoph Thoenissen, 2005. "Money and Monetary Policy in Stochastic General Equilibrium Models," CDMA Working Paper Series 200511, Centre for Dynamic Macroeconomic Analysis, revised 15 Feb 2007.
    4. Arnab Bhattacharjee & Christoph Thoenissen, 2007. "Money and Monetary Policy in DSGE Models," Money Macro and Finance (MMF) Research Group Conference 2006 78, Money Macro and Finance Research Group.

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