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Last edited on
Apr 18, 2024 by JJ.
Jan JOHANNES Feb 03,2023 Theses
Thesis:
Bachelor in Mathematics

Author:
Michael Schwind

Title:
Curve registration via penalized log-likelihood ratio testing

Supervisor:
Jan JOHANNES

Abstract:
Boosted by various applications in fields like medicine, computer vision or biology, we present in this thesis a framework for curve registration - meaning the problem of aligning curves by a monotonously transforming the argument and amplitude - via a penalized log-likelihood testing procedure. We show the asymptotic distribution of said testing procedure, which will give us a natural threshold to ensure a prescribed asymptotic significance level. Additionally we prove the consistency of the proposed test, i.e. the Power of the test converges to 1. To illustrate that the introduced methodology is applicable, we implemented the testing procedure in R and carried out a number of numerical experiments on synthetic data. The results of these experiments are in line with our theoretical results.
References:
O. Collier and A. S. Dalalyan. Curve registration by nonparametric goodness-of-fit testing, Journal of Statistical Planning and Inference, 162, 20-42, 2015.