Enno Mammen – författare

In these notes some results are presented for the asymptotic behavior of the bootstrap procedure. Bootstrap is a procedure for estimating (approximating) the distribution of a statistic. It is based on resampling and simulations. It was been introduced in Efron (1979) and in the last decade it has been discussed for a wide variety of statistical problems. Introductory are the articles Efron and Gong (1983) and Efron and Tibshirani (1986) and the book Helmers (1991b). Many applications of bootstrap are discussed in Efron (1982). Survey articles are Beran (1984b), Hinkley (1988), and Diciccio and Romano (1988a). For many classical decision problems (testing and estimation problems, prediction, construction of confidence regions) bootstrap has been compared with classical approximations based on mathematical limit theorems and expansions (for instance normal approximations, empirical Edgeworth expansions) (see for instance Bretagnolle (1983) and Beran (1982, 1984a, 1987, 1988), Abramovitch and Singh (1985), and Hall (1986a, 1988) ). An asymptotic treatment of bootstrap is contained in the book Beran and Ducharme (1991).A detailed analysis of bootstrap based on higher- order Edgeworth expansions has been carried out in the book Hall (1992). Recent publications on bootstrap can also be found in the conference volumes LePage and Billard (1992) and Joeckel, Rothe, and Sendler (1992). We will consider the application of bootstrap in three contexts : estimation of smooth functionals, nonparametric curve estimation, and linear models. We do not attempt a complete description of bootstrap in these areas.

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 6–8, 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 Reiβ and Enno Mammen. This interview gives some background on the life of Vladimir Spokoiny and his many scientific interests and motivations.