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We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally…

Applications · Statistics 2023-01-23 Niels Lundtorp Olsen , Bo Markussen , Lars Lau Rakêt

A commonly-used representation for motion prediction of actors is a sequence of waypoints (comprising positions and orientations) for each actor at discrete future time-points. While this approach is simple and flexible, it can exhibit…

Computer Vision and Pattern Recognition · Computer Science 2022-03-08 Zhaoen Su , Chao Wang , Henggang Cui , Nemanja Djuric , Carlos Vallespi-Gonzalez , David Bradley

We derive a simple expression for the probability of trajectories of a master equation. The expression is particularly useful when the number of states is small and permits the calculation of observables that can be defined as functionals…

Statistical Mechanics · Physics 2009-02-23 Andrew D. Jackson , Simone Pigolotti

Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and…

Methodology · Statistics 2025-05-06 Muye Nanshan , Nan Zhang , Jiguo Cao

We propose a new nonparametric procedure for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second- order) piecewise stationary process, which also identifies the components of…

Statistics Theory · Mathematics 2013-09-06 Philip Preuß , Ruprecht Puchstein , Holger Dette

We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…

Econometrics · Economics 2024-01-15 Chenlei Leng , Degui Li , Hanlin Shang , Yingcun Xia

Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…

Machine Learning · Statistics 2024-08-19 Sarbojit Roy , Malik Shahid Sultan , Hernando Ombao

Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…

Signal Processing · Electrical Eng. & Systems 2019-12-04 Bruno Scalzo Dees , Anh-Huy Phan , Danilo P. Mandic

Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…

Statistics Theory · Mathematics 2013-02-26 Stefan Fremdt , Lajos Horváth , Piotr Kokoszka , Josef G. Steinebach

In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…

Mathematical Physics · Physics 2024-03-26 Grégoire Sergeant-Perthuis

Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across…

Cellular Automata and Lattice Gases · Physics 2026-05-18 Matthew J Simpson , Michael J Plank

Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement independent reality of the system. The most simple case is observed in a three-dimensional…

Quantum Physics · Physics 2024-08-28 Holger F. Hofmann

The study of the dynamic behavior of cross-sectional ranks over time for functional data and the ranks of the observed curves at each time point and their temporal evolution can yield valuable insights into the time dynamics of functional…

Methodology · Statistics 2020-05-11 Yaqing Chen , Matthew Dawson , Hans-Georg Müller

Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses…

How does one find dimensions in multivariate data that are reliably expressed across repetitions? For example, in a brain imaging study one may want to identify combinations of neural signals that are reliably expressed across multiple…

Machine Learning · Statistics 2022-12-05 Lucas C. Parra , Stefan Haufe , Jacek P. Dmochowski

We consider the sampling problem for functional PCA (fPCA), where the simplest example is the case of taking time samples of the underlying functional components. More generally, we model the sampling operation as a continuous linear map…

Statistics Theory · Mathematics 2013-02-14 Arash A. Amini , Martin J. Wainwright

In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…

Machine Learning · Computer Science 2022-08-18 Povilas Daniušis , Shubham Juneja , Lukas Kuzma , Virginijus Marcinkevičius

Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…

Statistics Theory · Mathematics 2020-09-28 Sungkyu Jung

In this paper, we address the problem of dimension reduction for time series of functional data $(X_t\colon t\in\mathbb{Z})$. Such {\it functional time series} frequently arise, e.g., when a continuous-time process is segmented into some…

Statistics Theory · Mathematics 2015-06-03 Siegfried Hörmann , Łukasz Kidziński , Marc Hallin

We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…

Methodology · Statistics 2025-05-09 Kyunghee Han , Yeonjoo Park , Soo-Young Kim