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最优变点检测与定位AI 解读

Given a times series Y in Rn, with a piecewise constant mean and independent components, the twin problems of change-point detection and change-point localization, respectively amount to detecting the existence of times where the mean varies and estimating the positions of those change-points. In this work, we tightly characterize optimal rates for both problems and uncover the phase transition phenomenon from a global testing problem to a local estimation problem.…

基于均值中位数的稳健机器学习：理论与实践AI 解读

Median-of-means (MOM) based procedures have been recently introduced in learning theory (Lugosi and Mendelson (2019); Lecué and Lerasle (2017)). These estimators outperform classical least-squares estimators when data are heavy-tailed and/or are corrupted. None of these procedures can be implemented, which is the major issue of current MOM procedures (Ann. Statist. 47 (2019) 783–794). In this paper, we introduce minmax MOM estimators and show that they achieve the same…

多重检验的族级分离率AI 解读

Starting from a parallel between some minimax adaptive tests of a single null hypothesis, based on aggregation approaches, and some tests of multiple hypotheses, we propose a new second kind error-related evaluation criterion, as the core of an emergent minimax theory for multiple tests. Aggregation-based tests, proposed for instance by Baraud [Bernoulli 8 (2002) 577–606], Baraud, Huet and Laurent [Ann. Statist. 31 (2003) 225–251] or Fromont and Laurent [Ann. Statist. 34…

次高斯均值估计量AI 解读

We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a nonasymptotic point of view. In particular, we define estimators with a sub-Gaussian behavior even for certain heavy-tailed distributions. We also prove various impossibility results for mean estimators.

不同混合条件下平稳数据密度估计的最优模型选择AI 解读

We propose a block-resampling penalization method for marginal density estimation with nonnecessary independent observations. When the data are β or τ-mixing, the selected estimator satisfies oracle inequalities with leading constant asymptotically equal to 1. We also prove in this setting the slope heuristic, which is a data-driven method to optimize the leading constant in the penalty.