2005/11/20 by Catherine Loader, Loader, Catherine · 1 citation
Computer Science · Mathematics · #62G08 #62G32 (Primary) #62J02 #62J05 #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.math/0511502
openalex publication_date 2005/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The volume-of-tube formula was first introduced by Hotelling (1939), to solve significance of terms in nonlinear regression models. Since this pioneering paper, there has been significant work on extending the tube formula to more general settings, including multidimensional problems, and many new applications in statistical inference, including confidence bands in regression and smoothing models; applications to functional data analysis; testing in mixture models; and spatial scan analysis. Implementation of the tube formula requires numerical evaluation of certain problem-specific geometric constants that appear in Hotelling's formula and its extensions. The purpose of this note is to describe a software library, libtube, that performs the calculations. A variety of illustrative examples are given. Source code for the libtube library andexamples can be downloaded from http://www.herine.net/stat/libtube/.