866 citations · 1.2k across the 41 of their papers we have counts for
20 papers · 1 filter
Inference for Functional Data under Markov Constraints
Ulysse Naepels, Victor M. Panaretos
Smoothness has long been the dominant form of parsimony in functional data analysis, to the point of occasionally being conflated with the very notion of functional data. However,…
Statistical Inference for Bures-Wasserstein Flows
Leonardo V. Santoro, Victor M. Panaretos
We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hi…
The Functional Graphical Lasso
Kartik G. Waghmare, Tomas Masak, Victor M. Panaretos
We consider the problem of recovering conditional independence relationships between jointly distributed Hilbertian random elements given realizations thereof. We operate i…
Transportation-Based Functional ANOVA and PCA for Covariance Operators
Valentina Masarotto, Victor M. Panaretos, Yoav Zemel
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…
Functional Data Analysis with Rough Sample Paths?
Neda Mohammadi, Victor M. Panaretos
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…
Distribution-on-Distribution Regression via Optimal Transport Maps
Laya Ghodrati, Victor M. Panaretos
We present a framework for performing regression when both covariate and response are probability distributions on a compact interval . Our regression model is…
CovNet: Covariance Networks for Functional Data on Multidimensional Domains
Soham Sarkar, Victor M. Panaretos
Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical cha…
Inference and Computation for Sparsely Sampled Random Surfaces
Tomas Masak, Tomas Rubin, Victor Panaretos
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separab…
Spectral Simulation of Functional Time Series
Tomáš Rubín, Victor M. Panaretos
We develop methodology allowing to simulate a stationary functional time series defined by means of its spectral density operators. Our framework is general, in that it encompasses…
Random Surface Covariance Estimation by Shifted Partial Tracing
Tomas Masak, Victor M. Panaretos
The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computatio…
Functional Lagged Regression with Sparse Noisy Observations
Tomáš Rubín, Victor M. Panaretos
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 funct…
Testing for the Rank of a Covariance Operator
Anirvan Chakraborty, Victor M. Panaretos
How can we discern whether the covariance operator of a stochastic process is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confide…
Sparsely Observed Functional Time Series: Estimation and Prediction
Tomáš Rubín, Victor M. Panaretos
Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the const…
Statistical Aspects of Wasserstein Distances
Victor M. Panaretos, Yoav Zemel
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to…
Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes
Valentina Masarotto, Victor M. Panaretos, Yoav Zemel
Covariance operators are fundamental in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen--Loève expansion. These…
Regression with genuinely functional errors-in-covariates
Anirvan Chakraborty, Victor M. Panaretos
Contamination of covariates by measurement error is a classical problem in multivariate regression, where it is well known that failing to account for this contamination can result…
Functional Registration and Local Variations: Identifiability, Rank, and Tuning
Anirvan Chakraborty, Victor M. Panaretos
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…
Hybrid Regularisation of Functional Linear Models
Anirvan Chakraborty, Victor M. Panaretos
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 analy…
Functional Data Analysis by Matrix Completion
Marie-Hélène Descary, Victor M. Panaretos
Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, r…
A Conversation with David R. Brillinger
Victor M. Panaretos
David Ross Brillinger was born on the 27th of October 1937, in Toronto, Canada. In 1955, he entered the University of Toronto, graduating with a B.A. with Honours in Pure Mathemati…