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Projections on cones, chi-bar squared distributions, and Weyl's formula

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  • Lin, Yong
  • Lindsay, Bruce G.

Abstract

Using Weyl's formula for the volume of the tube about a manifold in the unit sphere, we show that the distribution of the squared length of the projection of the normal variate to any smooth convex cone is a mixture of chi-squared distributions and we give the explicit formulas for the weights. We also give the application of our work to circular cones.

Suggested Citation

  • Lin, Yong & Lindsay, Bruce G., 1997. "Projections on cones, chi-bar squared distributions, and Weyl's formula," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 367-376, April.
    • Handle: RePEc:eee:stapro:v:32:y:1997:i:4:p:367-376
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    Cited by:

    1. Delmas, Céline, 2003. "Projections on spherical cones, maximum of Gaussian fields and Rice's method," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 263-270, September.
    2. Satoshi Kuriki & Akimichi Takemura, 2000. "Some Geometry of the Cone of Nonnegative Definite Matrices and Weights of Associated X 2 Distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(1), pages 1-14, March.

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