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Second-Order Properties of a Two-Stage Fixed-Size Confidence Region for the Mean Vector of a Multivariate Normal Distribution

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  • Mukhopadhyay, N.

Abstract

We consider the classical fixed-size confidence region estimation problem for the mean vector[mu]in theNp([mu], [Sigma]) population where [Sigma] is unknown but positive definite. We write[lambda]1for the largest characteristic root of [Sigma] and assume that[lambda]1is simple. Moreover, we suppose that, in many practical applications, we will often have available a number[lambda]*(>0) and that we can assume[lambda]1>[lambda]*. Given this addi- tional, and yet very minimal, knowledge regarding[lambda]1, the two-stage procedure of Chatterjee (Calcutta Statist. Assoc. Bull.8(1959a), 121-148;9(1959b), 20-28;11(1962), 144-159) is revised appropriately. The highlight in this paper involves the verification ofsecond-order propertiesassociated with such revised two-stage estimation techniques, along with the maintenance of the nominal confidence coefficient.

Suggested Citation

  • Mukhopadhyay, N., 1999. "Second-Order Properties of a Two-Stage Fixed-Size Confidence Region for the Mean Vector of a Multivariate Normal Distribution," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 250-263, February.
    • Handle: RePEc:eee:jmvana:v:68:y:1999:i:2:p:250-263
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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. Robb Muirhead & Yasuko Chikuse, 1975. "Approximations for the distributions of the extreme latent roots of three matrices," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 473-478, December.
    3. Datta, S. & Mukhopadhyay, N., 1997. "On Sequential Fixed-Size Confidence Regions for the Mean Vector," Journal of Multivariate Analysis, Elsevier, vol. 60(2), pages 233-251, February.
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    Cited by:

    1. Nitis Mukhopadhyay & Tumulesh K. S. Solanky, 2012. "On Two-Stage Comparisons with a Control Under Heteroscedastic Normal Distributions," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 501-522, September.

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