Conference Agenda

Assume one wants to estimate the true parameter $vartheta_0$, which is the {it maximal} value {it minimizing} a function $M(vartheta)$ over $vartheta$. Let $M_n(vartheta)$ be a consistent estimator for $M(vartheta)$ uniformly in $vartheta$. Although uniform convergence holds, one cannot apply the argmin theorem in the non-unique minimum case. Using the {it maximal} value {it minimizing} the function $M_n(vartheta)$ over $vartheta$ generally does not give a consistent estimator. We consider a special case with real-valued parameter, and define a new consistent estimator. This method is then applied to estimate the gradual (smooth) change point $vartheta_0$ of a nonparametric regression model $Y=m(X)+varepsilon$ with real-valued covariates, and a continuous regression function $m$ with maximal value $vartheta_0$, where $m$ is zero.

Flow Matching (introduced by Lipman et. al.) and associated models have recently attracted significant interest due to their simulation-free training via a straightforward least squares criterion and the extremely broad and consequently adaptable underlying ordinary differential equation framework. Despite being a generative model that aims to mimic an unknown distribution, its possible applications extend far beyond the core task of generating new samples. The cheap generation of new samples opens the door to efficient distribution estimation, an essential component of forecasting tasks such as weather prediction. In this talk, we first adapt the Flow Matching method to smooth conditional density estimation. We show that the resulting estimator is closely related to th Nadaraya-Watson estimator. Then, we bridge the gap between proper scoring rules, the established method of evaluating predictions, and the fundamental concept of risk in statistical learning. Building on this, we show that the Nadaraya-Watson estimator achieves a minimax optimal anisotropic rate of convergence with respect to the risk associated with the Fourier score. In the end, we transfer this result to the Flow Matching estimator and demonstrate its capability in practice.

Consider data points sampled independently from the uniform distribution on a known symmetric convex body in high-dimensional Euclidean space with unknown location parameter. In this setting, the set of maximum likelihood estimators (MLE set) is a convex body containing the true location parameter. The goal of this talk is to present non-asymptotic upper and lower bounds for the diameter of the MLE set.

In this talk I will discuss recent work on two-sample testing under a local differential privacy constraint where a permutation procedure is used to calibrate the tests. While permutation testing is a classical resampling technique, popular due to its ease of implementation and uniform Type I error control, its use under local privacy constraints is complicated by the fact that access to the data is limited. In this work we design appropriate mechanisms for private data collection, both interactive and non-interactive, that allow for permutation tests. Our analysis shows that these lead to minimax optimal separation rates in both discrete and continuous settings, with interactive procedures being significantly more powerful. This is recent joint work with Alexander Kent and Yi Yu (https://arxiv.org/abs/2505.24811).