Detecting whether a stochastic process is finitely expressed in a basis
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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 ...
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 ...
EPFL2023
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We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...
2021
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 ...
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 ...
In the field of choice modeling, the availability of ever-larger datasets has the potential to significantly expand our understanding of human behavior, but this prospect is limited by the poor scalability of discrete choice models (DCMs): as sample sizes ...
Estimation of causal effects using machine learning methods has become an active research field in econometrics. In this paper, we study the finite sample performance of meta-learners for estimation of heterogeneous treatment effects under the usage of sam ...
2022
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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 ...
2019
The efficiency of stochastic particle schemes for large scale simulations relies on the ability to preserve a uniform distribution of particles in the whole physical domain. While simple particle split and merge algorithms have been considered previously, ...
2019
Covariance operators play a fundamental role in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loève expansion. These operators may themselves be subject to variation, for instance in con ...
