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Improved confidence regions based on Edgeworth expansions

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  • Withers, Christopher S.
  • Nadarajah, Saralees

Abstract

Let ŵ be a consistent estimate of w in Rp satisfying the standard cumulant expansion in powers of n−1 with asymptotic covariance n−1V. Then n1/2(ŵ−w) has the standard Edgeworth expansion about Np(0,V). We obtain from this the Edgeworth expansions for Tn(V)=n(ŵ−w)′V−1(ŵ−w) about χp2 and for its Studentized version, Tn(V̂). So, we obtain a confidence region for w of level α+O(n−2).

Suggested Citation

  • Withers, Christopher S. & Nadarajah, Saralees, 2012. "Improved confidence regions based on Edgeworth expansions," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4366-4380.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4366-4380
    DOI: 10.1016/j.csda.2012.03.019
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    References listed on IDEAS

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    1. 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.
    2. C. Withers, 1988. "Nonparametric confidence intervals for functions of several distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 727-746, December.
    3. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
    4. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
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    1. C. S. Withers, 2024. "5th-Order Multivariate Edgeworth Expansions for Parametric Estimates," Mathematics, MDPI, vol. 12(6), pages 1-28, March.
    2. Kakizawa, Yoshihide, 2016. "Some integrals involving multivariate Hermite polynomials: Application to evaluating higher-order local powers," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 162-168.
    3. Claudia Furlan & Cinzia Mortarino, 2020. "Comparison among simultaneous confidence regions for nonlinear diffusion models," Computational Statistics, Springer, vol. 35(4), pages 1951-1991, December.

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