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On hadamard differentiability of extended statistical functional

Author

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  • Ren, Jian-Jian
  • Sen, Pranab Kumar

Abstract

It has been shown ([6], Ph.D. dissertation, Harvard University) that the remainder term of a form of the Taylor expansion, involving Hadamard derivative, of the statistical functional is asymptotically negligible. This result is extended to a more general form with respect to weighted empirical processes in order to establish some (uniform) linear functional approximations, which is usually needed for drawing statistical conclusions (in a large sample).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:39:y:1991:i:1:p:30-43
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    Cited by:

    1. Ren, Jian-Jian & Sen, Pranab Kumar, 2001. "Second Order Hadamard Differentiability in Statistical Applications," Journal of Multivariate Analysis, Elsevier, vol. 77(2), pages 187-228, May.
    2. 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.
    3. Beutner, Eric & Zähle, Henryk, 2010. "A modified functional delta method and its application to the estimation of risk functionals," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2452-2463, November.
    4. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Karl B. Gregory & Soumendra N. Lahiri & Daniel J. Nordman, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 442-461, May.
    5. Freitag, Gudrun & Munk, Axel, 2005. "On Hadamard differentiability in k-sample semiparametric models--with applications to the assessment of structural relationships," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 123-158, May.
    6. Jian-Jian Ren, 1995. "Generalized Cramér-von Mises tests of goodness of fit for doubly censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 525-549, September.

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