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Asymptotic nonnull distributions of certain test criteria for a covariance matrix


  • Nagao, Hisao


Asymptotic expansions of the distributions of two test criteria concerning a covariance matrix are derived under local alternatives in terms of noncentral [chi]2 variates, and under the fixed alternative in terms of standard normal distribution function and its derivatives, respectively. Some numerical comparisons with the likelihood ratio criteria are made with these test criteria.

Suggested Citation

  • Nagao, Hisao, 1974. "Asymptotic nonnull distributions of certain test criteria for a covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 4(4), pages 409-418, December.
  • Handle: RePEc:eee:jmvana:v:4:y:1974:i:4:p:409-418

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    References listed on IDEAS

    1. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    2. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
    3. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
    4. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
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    Cited by:

    1. Shinto Eguchi, 1991. "A geometric look at nuisance parameter effect of local powers in testing hypothesis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 245-260, June.


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