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Second Order Hadamard Differentiability in Statistical Applications

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  • Ren, Jian-Jian
  • Sen, Pranab Kumar

Abstract

A formulation of the second-order Hadamard differentiability of (extended) statistical functionals and some related theoretical results are established. These results are applied to derive the limiting distributions of a class of generalized Cramér-von Mises type test statistics, which include some proposed new ones for the tests of goodness of fit in the 3-sample problems, the tests in linear regression models, and the tests of bivariate independence, as special cases.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:77:y:2001:i:2:p:187-228
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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. Ren Jian-Jian, 1994. "On Hadamard Differentiability And Its Application To R-Estimation In Linear Models," Statistics & Risk Modeling, De Gruyter, vol. 12(1), pages 1-22, January.
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    Cited by:

    1. Chiaki Hara, 2023. "Arrow-Pratt-Type Measure of Ambiguity Aversion," KIER Working Papers 1097, Kyoto University, Institute of Economic Research.
    2. 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.
    3. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.

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