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Fixed Width Confidence Region for the Mean of a Multivariate Normal Distribution

Author

Listed:
  • Nagao, Hisao
  • Srivastava, M. S.

Abstract

Srivastava gave an asymptotically efficient and consistent sequential procedure to obtain a fixed-width confidence region for the mean vector of any p-dimensional random vector with finite second moments. For normally distributed random vectors, Srivastava and Bhargava showed that the specified coverage probability is attained independent of the width, the mean vector, and the covariance matrix by taking a finite number of observations over and above T prescribed by the sequential rule. However, the problem of showing that E(T-n0) is bounded, where n0 is the sample size required if the covariance matrix were known, has not been available. In this paper, we not only show that it is bounded but obtain sharper estimates of E(T) on the lines of Woodroofe. We also give an asymptotic expansion of the coverage probability. Similar results have recently been obtained by Nagao under the assumption that the covariance matrix [Sigma]=[summation operator]ki=1Â [sigma]iAi and [summation operator]ki=1Â Ai=I, where Ai's are known matrices. We obtain the results of this paper under the sole assumption that the largest latent root of [Sigma] is simple.

Suggested Citation

  • Nagao, Hisao & Srivastava, M. S., 2002. "Fixed Width Confidence Region for the Mean of a Multivariate Normal Distribution," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 259-273, May.
  • Handle: RePEc:eee:jmvana:v:81:y:2002:i:2:p:259-273
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    References listed on IDEAS

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    1. Khatri, C. G., 1979. "Characterizations of multivariate normality II. Through linear regressions," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 589-598, December.
    2. Srivastava, M. S., 1973. "A sequential approach to classification: Cost of not knowing the covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 3(2), pages 173-183, June.
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    Cited by:

    1. Jin Zhang, 2017. "Minimum volume confidence sets for parameters of normal distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(3), pages 309-320, July.
    2. Xu, Jin & Gupta, Arjun K., 2006. "Improved confidence regions for a mean vector under general conditions," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1051-1062, November.

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