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Stochastics and Statistics Seminar

# Estimation and inference for error-in-operator model

## September 29, 2023 @ 11:00 am - 12:00 pm

Vladimir Spokoinyi (Humboldt University of Berlin)

E18-304

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Abstract:

We consider the Error-in-Operator (EiO) problem of recovering the source x signal from the noise observation Y given by the equation Y = A x + ε in the situation when the operator A is not precisely known. Instead, a pilot estimate \hat{A} is available. The study is motivated by Hoffmann & Reiss (2008), Trabs (2018) and by recent results on high dimensional regression with random design; see e.g., Tsigler, Bartlett (2020) (Benign overfitting in ridge regression; arXiv:2009.14286) Cheng, and Montanari (2022) (Dimension free ridge regression; arXiv:2210.08571), among many others. Examples of EiO include regression with error-in-variables and instrumental regression, stochastic diffusion, Markov time series, interacting particle systems. New approach is suggested which allows to obtain finite sample nearly sharp accuracy guarantees and incorporate the smoothness of the signal x and the operator A in a rather general form.

Bio:

Vladimir Spokoinyi received his PhD from the Department of Mechanics and Mathematics of the Lomonosov Moscow State University and did his Habilitation on “Statistical Experiments and Decisions: Asymptotic Theory” at the Humboldt University of Berlin. He is the head of the research group “Stochastic Algorithms & Nonparametric Statistics” of the Weierstrass Institute for Applied Analysis & Stochastics and Professor at the Humboldt University of Berlin. Spokoinyi’s main research interests lie in adaptive nonparametric smoothing and hypothesis testing, high dimensional data analysis and nonlinear time series, with applications to financial and imaging sciences. He is IMS Fellow and 2011 recipient of one of the multimillion-dollar Mega-grant projects awarded by the Russian government.

Bio:

Vladimir Spokoinyi received his PhD from the Department of Mechanics and Mathematics of the Lomonosov Moscow State University and did his Habilitation on “Statistical Experiments and Decisions: Asymptotic Theory” at the Humboldt University of Berlin. He is the head of the research group “Stochastic Algorithms & Nonparametric Statistics” of the Weierstrass Institute for Applied Analysis & Stochastics and Professor at the Humboldt University of Berlin. Spokoinyi’s main research interests lie in adaptive nonparametric smoothing and hypothesis testing, high dimensional data analysis and nonlinear time series, with applications to financial and imaging sciences. He is IMS Fellow and 2011 recipient of one of the multimillion-dollar Mega-grant projects awarded by the Russian government.