On Hotelling's Formula for the Volume of Tubes and Naiman's Inequality
Johnstone, Iain ; Siegmund, David
Ann. Statist., Tome 17 (1989) no. 1, p. 184-194 / Harvested from Project Euclid
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Two new derivations of the Hotelling-Naiman results on the volume of tubes about curves in spheres are presented. The first involves simple differential inequalities. The second is probabilistic, using the concept of upcrossing borrowed from the theory of Gaussian processes. The upcrossings method is extended to an harmonic regression problem not covered by the Hotelling-Naiman formulation.
Publié le : 1989-03-14
Classification:  Differential inequalities,  upcrossings,  62E15,  53A04 
@article{1176347010,
     author = {Johnstone, Iain and Siegmund, David},
     title = {On Hotelling's Formula for the Volume of Tubes and Naiman's Inequality},
     journal = {Ann. Statist.},
     volume = {17},
     number = {1},
     year = {1989},
     pages = { 184-194},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176347010}
}

Johnstone, Iain; Siegmund, David. On Hotelling's Formula for the Volume of Tubes and Naiman's Inequality. Ann. Statist., Tome 17 (1989) no. 1, pp.  184-194. http://gdmltest.u-ga.fr/item/1176347010/