Concept
Autocovariance
Related publications (34)
Transportation-based functional ANOVA and PCA for covariance operators
Victor Panaretos, Yoav Zemel, Valentina Masarotto
We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...
Inst Mathematical Statistics-Ims2024Positive Definite Completions and Continuous Graphical Models
This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...
EPFL2023Detecting whether a stochastic process is finitely expressed in a basis
Victor Panaretos, Neda Mohammadi Jouzdani
Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2023The DESI One-Percent Survey: Constructing Galaxy-Halo Connections for ELGs and LRGs Using Auto and Cross Correlations
In the current Dark Energy Spectroscopic Instrument (DESI) survey, emission line galaxies (ELGs) and luminous red galaxies (LRGs) are essential for mapping the dark matter distribution at < N(M)>. We measure the auto and cross correlation functions of ELGs ...
IOP Publishing Ltd2023On the rate of convergence for the autocorrelation operator in functional autoregression
Victor Panaretos, Alessia Caponera
We consider the problem of estimating the autocorrelation operator of an autoregressive Hilbertian process. By means of a Tikhonov approach, we establish a general result that yields the convergence rate of the estimated autocorrelation operator as a funct ...
ELSEVIER2022Functional estimation of anisotropic covariance and autocovariance operators on the sphere
Victor Panaretos, Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni, Alessia Caponera
We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...
2022Testing For The Rank Of A Covariance Operator
How can we discern whether the covariance operator of a stochastic pro-cess is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional dat ...
INST MATHEMATICAL STATISTICS-IMS2022Sparsely Observed Functional Time Series: Theory and Applications
Functional time series is a temporally ordered sequence of not necessarily independent random curves. While the statistical analysis of such data has been traditionally carried out under the assumption of completely observed functional data, it may well ha ...
EPFL2021Certified And Fast Computations With Shallow Covariance Kernels
Daniel Kressner, Stefano Massei
Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random fields have gained ...
AMER INST MATHEMATICAL SCIENCES-AIMS2020Pairwise Comparisons with Flexible Time-Dynamics
Matthias Grossglauser, Lucas Maystre, Victor Kristof
Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We achieve this by replac ...
ASSOC COMPUTING MACHINERY2019