Nonparametric maximum likelihood estimation for shifted curves

By B. Rønn. 2001

86 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/437b24bdbf5a5e6c2b6db2423c3bf17db7a6e4c2

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In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Functional Convex Averaging and Synchronization for Time-Warped Random Curves (2004, methodology): “In other recent developments, nonparametric maximum likelihood (MLE) was introduced by Rønn (2001), and local nonlinear adjustments were proposed by Kneip, Li, MacGibbon, and Ramsay (2000) to obtain the warping functions.”
Consistent estimation of a population barycenter in the Wasserstein space (2013, background): “In the one-dimensional case (d = 1), the model of shifted curves has applications in various fields such as as neurosciences [32] or biology [30].”
Characterization of barycenters in the Wasserstein space by averaging optimal transport maps (2012, background): “benchmark for the statistical analysis of deformable models. In the one-dimensional case (d= 1), the model of shifted curves has applications in various ﬁelds such as as neurosciences [32] or biology [30]. Let q0 : Rd → R+ be a probability density function with compact support included in [−A,A]d fo”
Self‐modelling warping functions (2004, methodology): “…and Gasser, 1992), shape invariant modelling (Kneip and Engel, 1995), continuous monotone registration (Ramsay and Li, 1998), dynamic time warping (Wang and Gasser, 1999), local regression (Kneip et al., 2000) and maximum likelihood registration (Rønn, 2001), the last restricted to random shifts.”
Pairwise curve synchronization for functional data (2008, background): “…developments in curve registration and warping include self-modelling warping (Gervini & Gasser, 2004); nonparametric maximum-likelihood warping (Rønn, 2001; Gervini & Gasser, 2005); functional convex synchronization (Liu & Müller, 2004); dynamic time warping (Wang & Gasser, 1997, 1999), and a…”
Functional Modelling and Classification of Longitudinal Data. (2005, methodology): “If we adopt the non-parametric FDA point of view, basic statistical notions such as mean, variance, correlation and regression need to be developed from scratch again, as the classical notions do not lend themselves to straightforward extensions to the functional case.”
Curve alignment by moments (2007, background): “…a continuous function of γ̂n and µ (l,k) Ẑn is a continuous function of θ̂n [by (A-1)], f is continuous and, hence, (14) implies that f(η̂n′′(ω)(ω), t)→ f(η̂ ∗(ω), t) ∀t(15) and µ (l,k) Ẑn (ω)→ µ (l,k) Z∗ for l = 1, . . . ,L and k = 1, . . . ,Kl.(16) Now, (11) and (15) imply that f(η0, t) =…”
Functional Modelling and Classification of Longitudinal Data * (2005, methodology): “…(Gasser & Kneip, 1995), Procrustes method (Ramsay & Li, 1998), time acceleration models (Capra & Müller, 1997), maximum likelihood based alignment (Rønn, 2001) and other forms of curve registration (Wang & Gasser, 1997, 1998, 1999; Kneip et al., 2000), and recently timesynchronization of random…”