Publications by Victor Panaretos

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We propose a nonparametric method for constructing multivariate kernels tuned to the configuration of the sample, for density estimation in R-d, d moderate. The motivation behind the approach is to break down the construction of the kernel into two parts: ...

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Omega of a rectangular domain I x I to a covariance kernel on the entire domain I x I. For a broad class of domains Omega call ...

We develop a canonical framework for the study of the problem of registration of multiple point processes subjected to warping, known as the problem of separation of amplitude and phase variation. The amplitude variation of a real random function {Y(x) : x ...

Motivated by the problem of inferring the molecular dynamics of DNA in solution, and linking them with its base-pair composition, we consider the problem of comparing the dynamics of functional time series (FTS), and of localizing any inferred differences ...

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

Given two samples of continuous zero-mean iid Gaussian processes on [0,1], we consider the problem of testing whether they share the same covariance structure. Our study is motivated by the problem of determining whether the mechanical properties of short ...

We study the positive-definite completion problem for kernels on a variety of domains and prove results concerning the existence, uniqueness, and characterization of solutions. In particular, we study a special solution called the canonical completion whic ...

We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is observed only on a subinterval of length , one has no statistical information on ...

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address ...

We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fréchet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed random measures and ...

We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of Double-struck capital R. An order-1 autoregressive model in this context is to be understood as a Markov chain, where ...

We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on

\mathbb{R}^3

is to be recovered from observation of finitely many of its two-dimensional projections in random and unobserv ...

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 ...

The nonparametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are typically alleviated by ...

We develop theory and methodology for the problem of nonparametric registration of functional data that have been subjected to random deformation (warping) of their time scale. The separation of this phase variation ("horizontal" variation) from the amplit ...

We consider the problem of estimation in a partially observed discrete-time Galton-Watson branching process, focusing on the first two moments of the offspring distribution. Our study is motivated by modelling the counts of new cases at the onset of a stoc ...

A framework is introduced for the study of general Radon shape diffusions, that is, shape diffusions induced by projections of randomly rotating shapes. This is done via a convenient representation of unoriented Radon shape diffusions in (unoriented) D.G. ...

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 ...

We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which gen ...

Let X={Xu}u is an element of U be a real-valued Gaussian process indexed by a set U. We show that X can be viewed as a graphical model with an uncountably infinite graph, where each Xu is a vertex. This graph is characterized by the reproducing property of ...

Victor Panaretos

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Nonparametric Construction of Multivariate Kernels

The Completion Of Covariance Kernels

Amplitude And Phase Variation Of Point Processes

Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles

THE POSITIVE-DEFINITE COMPLETION PROBLEM

Recovering covariance from functional fragments

CovNet: Covariance networks for functional data on multidimensional domains

Fréchet means and Procrustes analysis in Wasserstein space

On distributional autoregression and iterated transportation

On Random Tomography with Unobservable Projection Angles

Testing For The Rank Of A Covariance Operator

Separable expansions for covariance estimation via the partial inner product

Functional registration and local variations: Identifiability, rank, and tuning

Asymptotic Inference For Partially Observed Branching Processes

Representation of Radon Shape Diffusions via Hyperspherical Brownian Motion

On the rate of convergence for the autocorrelation operator in functional autoregression

Fourier Analysis Of Stationary Time Series In Function Space

Continuously indexed graphical models