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09/18/2023
The Positive-Definite Completion Problem
We study the positive-definite completion problem for kernels on a varie...
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06/04/2023
The Functional Graphical Lasso
We consider the problem of recovering conditional independence relations...
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05/27/2023
Transportation of Measure Regression in Higher Dimensions
We present an optimal transport framework for performing regression when...
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05/24/2023
Large Sample Theory for Bures-Wasserstein Barycentres
We establish a strong law of large numbers and a central limit theorem i...
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03/16/2023
On Distributional Autoregression and Iterated Transportation
We consider the problem of defining and fitting models of autoregressive...
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03/01/2023
A Karhunen-Loève Theorem for Random Flows in Hilbert spaces
We develop a generalisation of Mercer's theorem to operator-valued kerne...
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02/05/2023
Continuously Indexed Graphical Models
Let X = {X_u}_u ∈ U be a real-valued Gaussian process indexed by a set U...
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12/09/2022
Transportation-Based Functional ANOVA and PCA for Covariance Operators
We consider the problem of comparing several samples of stochastic proce...
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06/03/2022
Minimax Rate for Optimal Transport Regression Between Distributions
Distribution-on-distribution regression considers the problem of formula...
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02/18/2022
On the rate of convergence for the autocorrelation operator in functional autoregression
We consider the problem of estimating the autocorrelation operator of an...
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12/23/2021
Nonparametric Estimation of Covariance and Autocovariance Operators on the Sphere
We propose nonparametric estimators for the second-order central moments...
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11/02/2021
Detecting Whether a Stochastic Process is Finitely Expressed in a Basis
Is it possible to detect if the sample paths of a stochastic process alm...
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10/27/2021
Nonparametric Estimation for SDE with Sparsely Sampled Paths: an FDA Perspective
We consider the problem of nonparametric estimation of the drift and dif...
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07/15/2021
The Completion of Covariance Kernels
We consider the problem of positive-semidefinite continuation: extending...
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05/25/2021
Functional Data Analysis with Rough Sampled Paths?
Functional data are typically modeled as sampled paths of smooth stochas...
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04/19/2021
Distribution-on-Distribution Regression via Optimal Transport Maps
We present a framework for performing regression when both covariate and...
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04/11/2021
CovNet: Covariance Networks for Functional Data on Multidimensional Domains
Covariance estimation is ubiquitous in functional data analysis. Yet, th...
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07/23/2020
Principal Separable Component Analysis via the Partial Inner Product
The non-parametric estimation of covariance lies at the heart of functio...
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07/16/2020
Spectral Simulation of Functional Time Series
We develop methodology allowing to simulate a stationary functional time...
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12/30/2019
Spatiotemporal Covariance Estimation by Shifted Partial Tracing
We consider the problem of covariance estimation for replicated space-ti...
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05/17/2019
Functional Lagged Regression with Sparse Noisy Observations
A (lagged) time series regression model involves the regression of scala...
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01/08/2019
What is the dimension of a stochastic process? Testing for the rank of a covariance operator
How can we discern whether a mean-square continuous stochastic process i...
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11/15/2018
Sparsely Observed Functional Time Series: Estimation and Prediction
Functional time series analysis, whether based on time of frequency doma...
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06/14/2018
Statistical Aspects of Wasserstein Distances
Wasserstein distances are metrics on probability distributions inspired ...
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01/06/2018
Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes
Covariance operators are fundamental in functional data analysis, provid...
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12/12/2017