One of the most basic problems in statistics is how to estimate the expected value of a distribution, based on a sample of independent random draws. When the goal is to minimize the length of a confidence interval, the usual empirical mean has a sub-optimal performance, especially for heavy-tailed distributions. In this talk we discuss some estimators that achieve a sub-Gaussian performance under general conditions. The multivariate scenario turns out to be more challenging. We present an estimator with near-optimal performance. We also discuss how these ideas extend to regression function...

# PACM/Applied Mathematics Colloquium

The PACM Colloquium hosts seminars in the field of applied mathematics. Domains of interest include computational fluid dynamics and material science, dynamical systems, numerical analysis and fast algorithms, stochastic problems and stochastic analysis, graph theory and applications, mathematical biology, financial mathematics and mathematical approaches to signal analysis, image processing and information theory.http://www.pacm.princeton.edu/seminars

Organizer(s):

For more information about this seminar, contact Amit Singer

**Please click on colloquium title for complete abstract.**

October 23, 2017

4:00pm - 5:00pm

##### Mean estimation: median-of-means tournaments

Location

Fine Hall 214

Speaker: GĂˇbor Lugosi,

ICREA & Pompeu Fabra University, Spain

ICREA & Pompeu Fabra University, Spain

November 6, 2017

4:00pm - 5:00pm

##### TBA - Cesare Tronci

Location

Fine Hall 214

Speaker: Cesare Tronci,

University of Surrey, Guilford, UK

University of Surrey, Guilford, UK

November 20, 2017

4:00pm - 5:00pm

##### TBA - Cyrill Muratov

Location

Fine Hall 214

Speaker: Cyrill Muratov,

NJ Institute of Technology

NJ Institute of Technology

November 27, 2017

4:00pm - 5:00pm

##### Self-similar structure of caustics and shock formation

Location

Fine Hall 214

Speaker: Jens Eggers,

Bristol University

Bristol University