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Accurate tests and intervals based on nonlinear cusum statistics

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  • Withers, Christopher S.
  • Nadarajah, Saralees

Abstract

Suppose that we are monitoring incoming observations for a change in mean via a cusum test statistic. The usual nonparametric methods give first and second order approximations for the one- and two-sided cases. Withers and Nadarajah [2009. Accurate tests and intervals based on linear cusum statistics. Statistics and Probability Letters 79, 689-697] showed how to improve the order of these approximations for linear statistics. Here, an extension is provided for nonlinear statistics with non-zero asymptotic variances. This involves development of two calculi analogous to that of von Mises.

Suggested Citation

  • Withers, Christopher S. & Nadarajah, Saralees, 2009. "Accurate tests and intervals based on nonlinear cusum statistics," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2242-2250, November.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:21:p:2242-2250
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    References listed on IDEAS

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    1. Ren, Jian-Jian & Sen, Pranab Kumar, 1991. "On hadamard differentiability of extended statistical functional," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 30-43, October.
    2. Withers, Christopher S. & Nadarajah, Saralees, 2009. "Accurate tests and intervals based on linear cusum statistics," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 689-697, March.
    3. Ren, J. J. & Sen, P. K., 1995. "Hadamard Differentiability on D[0,1]p," Journal of Multivariate Analysis, Elsevier, vol. 55(1), pages 14-28, October.
    4. 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.
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