统计理论

The problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional continuous time stationary stochastic process is considered. Estimates are based on observations of the…

This paper focuses on the problem of the mean square optimal estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence. Estimates are based on observations of the sequence with…

We establish finite-sample error bounds in expectation for transformed Fr\'echet means in Hadamard spaces under minimal assumptions. Transformed Fr\'echet means provide a unifying framework encompassing classical and robust notions of…

We study the problem of detecting and localizing multiple changes in the mean parameter of a Banach space-valued time series. The goal is to construct a collection of narrow confidence intervals, each containing at least one (or exactly…

Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…

We study the estimation of the ATE in randomized controlled trials under a dynamically evolving interference structure. This setting arises in applications such as ride-sharing, where drivers move over time, and social networks, where…

Uncertainty quantification (UQ) for adaptively collected data, such as that coming from adaptive experiments, bandits, or reinforcement learning, is necessary for critical elements of data collection such as ensuring safety and conducting…

In this paper, we analyze the asymptotic behavior of a system of interacting reinforced stochastic processes $({\bf Z}_n, {\bf N}_n)_n$ on a directed network of $N$ agents. The system is defined by the coupled dynamics ${\bf…

This paper presents a rigorous resolution of the Borel-Kolmogorov paradox using the Maximum Entropy Principle. We construct a metric-based framework for Bayesian inference that uniquely extends conditional probability to events of null…

Positive dependencies have been compared in the literature under rather strong assumptions such as equality of conditional distributions, exchangeability, or stationarity. We establish supermodular ordering results for distributions that…

We consider the framework of penalized estimation where the penalty term is given by a real-valued polyhedral gauge, which encompasses methods such as LASSO, generalized LASSO, SLOPE, OSCAR, PACS and others. Each of these estimators is…

We consider the adaptive Lasso estimator with componentwise tuning in the framework of a low-dimensional linear regression model. In our setting, at least one of the components is penalized at the rate of consistent model selection and…

We establish non-asymptotic efficiency guarantees for tensor decomposition-based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference, the estimation of the full distributional…

We provide a unified approach to MM-estimation with auxiliary scale for balanced linear models with structured covariance matrices. This approach leads to estimators that are highly robust against outliers and highly efficient for normal…

Statistical inference on histograms and frequency counts plays a central role in categorical data analysis. Moving beyond classical methods that directly analyze labeled frequencies, we introduce a framework that models the multiset of…

The problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequence with periodically stationary increments based on observations of the sequence with a periodically stationary noise is…

Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…

We first study the generalization error of models that use a fixed feature representation (frozen intermediate layers) followed by a trainable readout layer. This setting encompasses a range of architectures, from deep random-feature models…

The control variates method is a classical variance reduction technique for Monte Carlo estimators that exploits correlated auxiliary variables without introducing bias. In many applications, the quantity of interest can be expressed as a…

Gaussian mixture models (GMMs) are fundamental statistical tools for modeling heterogeneous data. Due to the nonconcavity of the likelihood function, the Expectation-Maximization (EM) algorithm is widely used for parameter estimation of…