Geodesic
Estimating an even spherical measure from its sine transform
Applications of Mathematics, Tome 54 (2009) no. 1, pp. 67-78

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MR Zbl
To reconstruct an even Borel measure on the unit sphere from finitely many values of its sine transform a least square estimator is proposed. Applying results by Gardner, Kiderlen and Milanfar we estimate its rate of convergence and prove strong consistency. We close this paper by giving an estimator for the directional distribution of certain three-dimensional stationary Poisson processes of convex cylinders which have applications in material science.
To reconstruct an even Borel measure on the unit sphere from finitely many values of its sine transform a least square estimator is proposed. Applying results by Gardner, Kiderlen and Milanfar we estimate its rate of convergence and prove strong consistency. We close this paper by giving an estimator for the directional distribution of certain three-dimensional stationary Poisson processes of convex cylinders which have applications in material science.
DOI : 10.1007/s10492-009-0005-9
Classification : 52A22, 60D05, 60G10, 62H11, 62M30, 65D15
Keywords: Boolean model; convex cylinder; direction distribution; least square estimator; parameter estimation; Poisson process; spherical measure; sine transform 
Hoffmann, Lars Michael. Estimating an even spherical measure from its sine transform. Applications of Mathematics, Tome 54 (2009) no. 1, pp. 67-78. doi: 10.1007/s10492-009-0005-9
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