/tags/2025-winter/index.xml 2025 Winter - McGill Statistics Seminars

2025 Winter

  • The empirical copula process on classes of non-rectangular sets

    Michaël Lalancette · Feb 7, 2025

    Date: 2025-02-07

    Time: 15:30-16:30 (Montreal time)

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/81032144286

    Meeting ID: 810 3214 4286

    Passcode: None

    Abstract:

    The copula of a random vector with unknown marginals can be estimated non-parametrically by the empirical copula, akin to the empirical distribution. However, the asymptotic analysis of the empirical copula is made considerably more involved than that of the empirical distribution by the use of pseudo-observations, involving the marginal empirical distribution functions. In particular, it is still unknown whether the empirical copula evaluated at a non-rectangular set is asymptotically normally distributed. In this work, sufficient conditions under which this is the case are identified. The result is extended to a Donsker theorem for the empirical copula indexed by an infinite collection of non-rectangular sets. Some aspects of the proof involving geometric measure theory will be discussed. Based on ongoing joint work with Axel Bücher, Johan Segers and Stanislav Volgushev.

  • Multivariate Extremes Generator by Statistical Learning

    Nicolas Lafon · Jan 31, 2025

    Date: 2025-01-31

    Time: 15:30-16:30 (Montreal time)

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/88929152266

    Meeting ID: 889 2915 2266

    Passcode: None

    Abstract:

    Generating realistic extremes from an observational dataset is crucial when trying to estimate the risks associated with the occurrence of future extremes, possibly of greater magnitude than those already observed. Generative approaches from the machine learning community are not applicable to extreme samples without careful adaptation. On the other hand, asymptotic results from extreme value theory provide a theoretical framework for modeling multivariate extreme events, through the notion of multivariate regular variation. Bridging these two fields, this presentation details a variational autoencoder approach for sampling multivariate distributions with heavy tails, i.e., distributions likely to exhibit extremes of particularly large intensities.

  • Tree Pólya Splitting distributions for multivariate count data

    Samuel Valiquette · Jan 17, 2025

    Date: 2025-01-17

    Time: 15:30-16:30 (Montreal time)

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/82903352833

    Meeting ID: 829 0335 2833

    Passcode: None

    Abstract:

    The analysis of multivariate count data is fundamental in various fields. An appropriate model must be able to be flexible enough for inducing correlation, but also simple for inference and interpretation. One such model is the Pólya Splitting model, which randomly decomposes the sum of a discrete vector into its components. This simple approach offers several compelling properties. However, it imposes the constraint that the dependency structure must be identical across all components. To overcome this limitation, a generalization of this model called Tree Pólya splitting is proposed. For this new model, the splitting process is represented by a tree structure, allowing for more flexibility. In this seminar, we will define the Tree Pólya Splitting model and explore various properties, including marginal distributions, factorial moments, and the dependency structure.