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A test for singularity

Author

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  • Frigyesi, Attila
  • Hössjer, Ola

Abstract

The Lp-norm and other functionals of the kernel estimate of density functions (as functions of the bandwidth) are studied as means to test singularity. Given an absolutely continuous distribution function, the Lp-norm, and the other studied functionals, will converge under some mild side-constraints as the bandwidth decreases. In the singular case, the functionals will diverge. These properties may be used to test whether data comes from an arbitrarily large class of absolutely continuous distributions or not.

Suggested Citation

  • Frigyesi, Attila & Hössjer, Ola, 1998. "A test for singularity," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 215-226, October.
    • Handle: RePEc:eee:stapro:v:40:y:1998:i:3:p:215-226
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    Cited by:

    1. Zinde-Walsh, Victoria, 2008. "Kernel Estimation When Density May Not Exist," Econometric Theory, Cambridge University Press, vol. 24(3), pages 696-725, June.

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