For more than two centuries, least-squares regression has been a cornerstone of statistical practice, while classical nonparametric smoothing methods have long served as standard tools for analysing complex data. In this workshop, we will revisit these methods from a modern perspective and ask: Are we making the best possible use of them? Recent work in statistical theory by Richard Samworth and others shows that these familiar methods can often be improved by incorporating additional structural information, such as shape constraints or properties of the underlying error distribution.

This two-day workshop, led by Richard Samworth, will explore recent developments in distributionally adaptive statistical methods. Richard Samworth is Professor of Statistical Science and Director of the Statistical Laboratory at the University of Cambridge. A Fellow of the Royal Society, he is the recipient of numerous distinctions, including the COPSS Presidents' Award, the David Cox Medal, and, in 2025, the Royal Statistical Society Guy Medal in Silver. His research has made fundamental contributions to nonparametric statistics, statistical learning theory, and high-dimensional methodology, particularly in shape-constrained estimation and adaptive nonparametric procedures. A defining feature of his research is the combination of rigorous theoretical guarantees with methods designed to be computationally efficient and practically applicable.

• The first day will focus on linear regression and shape-constrained estimation. Starting from the classical least-squares framework, the workshop will examine how structural information, including monotonicity, can be used to improve estimation and inference.
• The second day will turn to nonparametric regression. It will begin with local polynomial methods and their theoretical foundations before introducing recent extensions, including Outrigger local polynomial regression, which adapts to the underlying error distribution while retaining strong theoretical guarantees.

The theoretical lectures will be complemented by practical sessions in R and Python, allowing participants to apply the methods discussed during the workshop. A joint poster session, with a particular focus on early-career researchers, will provide an opportunity to present ongoing work, exchange ideas across disciplines, and receive feedback from other participants and senior researchers. The poster session on Monday and the plenary talk on Tuesday will also be open to researchers from the university and neighbouring institutions.

The workshop is primarily intended for doctoral candidates and postdoctoral researchers from the KCDS Graduate School and the Heidelberg Graduate School MathComp, as well as members of the Helmholtz Association and researchers in related fields who have a strong interest in modern mathematical statistics.
Participants will gain insight into current developments in adaptive statistical methodology and their connections to broader challenges in statistical learning and modern data analysis.

The workshop and keynote lecture are organized by the Institute of Statistics (STAT) in cooperation with MathSEE / KCDS and HGS MathComp at Heidelberg University. The workshop was made possible through Course Funding from HIDA, which supported its development and implementation.