Using an expression for the expected number of local maxima of a random field, we derive an upper bound for the volume of a tube about a manifold in the unit sphere and show that under certain conditions our bound agrees with the evaluation of the tube volume in Weyl's formula. Applications to tests and confidence regions in nonlinear regression are discussed.
"The Expected Number of Local Maxima of a Random Field and the Volume of Tubes." Ann. Statist. 21 (4) 1948 - 1966, December, 1993. https://doi.org/10.1214/aos/1176349404