Functional Convex Averaging and Synchronization for Time-Warped Random Curves

• Published in: Journal of the American Statistical Association Vol. 99; no. 467; pp. 687 - 699
• Main Authors: Liu, Xueli, Müller, Hans-Georg
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.09.2004; American Statistical Association; Taylor & Francis Ltd
• Subjects: Alignment; Applications; Confidence band; Convex calculus; Curve registration; Data analysis; Data collection; Data sampling; Exact sciences and technology; Functional data analysis; General topics; Growth curves; Growth spurts; Landmarks; Limit theorems; Mathematical models; Mathematics; Methodology; Nonparametric function estimation; Probability; Probability and statistics; Probability theory and stochastic processes; Random sampling; Registration; Sample mean; Sample statistics; Sample variance; Sciences and techniques of general use; Smoothing; Space based observatories; Statistical discrepancies; Statistical methods; Statistics; Stochastic models; Stochastic process; Stochastic processes; Theory and Methods; Time; Warping; Weak convergence; Monotonic function; Statistical analysis; Function space; Image processing; Confidence limit; Average; Time scale; Median; Space time; Stochastic process; Mean estimation; Implementation; Confidence interval; Limit theorem; Functional; Statistical method; Response time; Experimental unit; Cross sectional study; Asymptotic approximation; Random function; Application

Data that can be best described as a sample of curves are now fairly common in science and engineering. When the dynamics of development, growth, or response over time are at issue, subjects or experimental units may experience events at different temporal paces. For functional data where trajectori...