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

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.

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Year of publication:	1997
Authors:	Lin, Yong ; Lindsay, Bruce G.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 32.1997, 4, p. 367-376
Publisher:	Elsevier
Keywords:	Weyl's formula Tube volume Chi-bar squared distribution Projection Convex cone

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005254837