Publications by Victor Panaretos

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Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...

We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse problem arising in da ...

A functional (lagged) time series regression model involves the regression of scalar response time series on a time series of regressors that consists of a sequence of random functions. In practice, the underlying regressor curve time series are not always ...

Functional time series analysis, whether based on time or frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless, as is often the c ...

The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite-dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose inverse is by defi ...

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 ...

The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the covariance, even ...

We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a regularised estimation p ...

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 ...

We revisit the problem of extending the notion of principal component analysis (PCA) to multivariate datasets that satisfy nonlinear constraints, therefore lying on Riemannian manifolds. Our aim is to determine curves on the manifold that retain their cano ...

Inferences related to the second-order properties of functional data, as expressed by covariance structure, can become unreliable when the data are non-Gaussian or contain unusual observations. In the functional setting, it is often difficult to identify a ...

Nonparametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these issues in the de ...

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 ...

We develop a doubly spectral representation of a stationary functional time series, and study the properties of its empirical version. The representation decomposes the time series into an integral of uncorrelated frequency components (Cramer representatio ...

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in order to recover th ...

Single-particle electron microscopy is a modern technique that biophysicists employ to learn the structure of proteins. It yields data that consist of noisy random projections of the protein structure in random directions, with the added complication that ...

We consider the problem of inferring the potential of an epidemic for escalating into a pandemic on the basis of limited observations in its initial stages. Classical results of Becker & Hasofer (J. R. Statist. Soc. B, 59, 415-29) illustrate that frequenti ...

Covariance operators are fundamental in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loeve expansion. These operators may themselves be subject to variation, for instance in contexts wh ...

We develop a generalisation of Mercer’s theorem to operator-valued kernels in infinite dimensional Hilbert spaces. We then apply our result to prove a Karhunen-Loève theorem, valid for mean-square continuous random functions valued in a separable Hilbert s ...

Distribution-on-distribution regression considers the problem of formulating and es-timating a regression relationship where both covariate and response are probability distributions. The optimal transport distributional regression model postulates that th ...

Victor Panaretos

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Functional data analysis with rough sample paths?

Statistical Unfolding Of Elementary Particle Spectra: Empirical Bayes Estimation And Bias-Corrected Uncertainty Quantification

Functional lagged regression with sparse noisy observations

Sparsely observed functional time series: estimation and prediction

Methodology And Convergence Rates For Functional Time Series Regression

Transportation-based functional ANOVA and PCA for covariance operators

Random Surface Covariance Estimation by Shifted Partial Tracing

Hybrid regularisation and the (in)admissibility of ridge regression in infinite dimensional Hilbert spaces

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Principal Flows

Dispersion operators and resistant second-order functional data analysis

Inference and Computation for Sparsely Sampled Random Surfaces

Detecting whether a stochastic process is finitely expressed in a basis

Cramer-Karhunen-Loeve representation and harmonic principal component analysis of functional time series

Statistical Aspects of Wasserstein Distances

Sparse Approximations Of Protein Structure From Noisy Random Projections

Frequentist estimation of an epidemic's spreading potential when observations are scarce

Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes

A Karhunen–Loève theorem for random flows in Hilbert spaces

Minimax rate for optimal transport regression between distributions