Title: Statistical Shape Methodology for the Analysis of Helices

Author(s): John T. Kent, Kanti V. Mardia and Mai F. Alfahad
Issue: Volume 81 Series A Part 1 Year 2019
Pages: 8 -- 32
Consider a helix in three-dimensional space along which a sequence of equally spaced points is observed, subject to statistical noise. For data coming from a single helix, a two-stage algorithm based on a profile likelihood is developed to compute the maximum likelihood estimate of the helix parameters. Statistical properties of the estimator are studied and comparisons are made to other estimators found in the literature. Next a likelihood ratio test is developed to test if there is a change point in the helix, splitting the data into two sub-helices. The shapes of protein α-helices are used to illustrate the methodology.
Primary 62H11; Secondary 62P10, 92C40
Keywords and phrases: Change point, Helix axis, Kinked helix, Principal component analysis, Procrustes analysis, Shape analysis