This book contains contributions from the participants of the international conference Foundations of Modern Statistics which took place at Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, during November 68, 2019, and at Higher School of Economics (HSE University), Moscow, during November 30, 2019. The events were organized in honor of Professor Vladimir Spokoiny on the occasion of his 60th birthday. Vladimir Spokoiny has pioneered the field of adaptive statistical inference and contributed to a variety of its applications. His more than 30 years of research in the field of mathematical statistics had a great influence on the development of the mathematical theory of statistics to its present state. It has inspired many young researchers to start their research in this exciting field of mathematics.

The papers contained in this book reflect the broad field of interests of Vladimir Spokoiny: optimal rates and non-asymptotic bounds in nonparametrics, Bayes approaches from a frequentist point of view, optimization, signal processing, and statistical theory motivated by models in applied fields. Materials prepared by famous scientists contain original scientific results, which makes the publication valuable for researchers working in these fields. The book concludes by a conversation of Vladimir Spokoiny with Markus Rei and Enno Mammen. This interview gives some background on the life of Vladimir Spokoiny and his many scientific interests and motivations.

Inhalt
Optimal rates and non-asymptotic bounds in nonparametrics: Z. Harchaoui, A. Juditsky, A. Nemirovski, D. Ostrovskii, Adaptive Denoising of Signals with Local Shift-Invariant Structure.- A. Dubois, Thomas B. Berret, C. Butucea, Goodness-of-fit testing for Hölder continuous densities under local differential privacy.- G. Blanchard and J.ean-Baptiste Fermanian, Nonasymptotic signal detection and two-sample tests in high dimension.- Sara van de Geer and P. Hinz, The Lasso with structured design and entropy of (absolute) convex hulls.- M. Hiabu, E. Mammen and Joseph-Theo Meyer, Local linear smoothing in additive models as data projection.- S. Ayvazyan and V. Ulyanov, A multivariate CLT for typical weighted sums with rate of convergence of order O(1/n).- Estimation of matrices and subspaces: F. Götze, A. Tikhomirov, D. Timushev, Rate of convergence for sample covariance sparse matrices.- M. Wahl, Van Trees inequality, group equivariance, and estimation of principal subspaces.- D. Belomestny, E. Krymova, Sparse constrained projection approximation subspace tracking Nonparametric and semiparametric Bayes statistics.- Natalia Bochkina: Bernstein - von Mises theorem and misspecified models: a review.- M. Panov, On accuracy of Gaussian approximation in Bayesian semiparametric problems.- Statistical theory motivated by applications: M. Bl ehaut, X. D'Haultfuille, J er emy L'Hour, A. B. Tsybakov, An alternative to synthetic control for models with many covariates under sparsity.- C. Breunig, X. Chen, Adaptive Estimation of Quadratic Functionals in Nonparametric Instrumental Variable Models.- G. Kulaitis, A. Munk and F. Werner, A minimax testing perspective on spatial statistical resolution in microscopy.- Optimisation: P. Dvurechensky, A. Gasnikov, A. Tyurin and V. Zholobov, Unifying Framework for Accelerated Randomized Methods in Convex Optimization.- K. Khowaja, M. Shcherbatyy and W. Karl Härdle. Surrogate Models for Optimization of Dynamical Systems.- Interview with Vladimir Spokoiny.