[Paper Review] Asymptotics: Particles, Processes and Inverse Problems. Festschrift for Piet Groeneboom

Eric Cator, Geurt Jongbloed+3 more|Sep 11, 2007

Scientific Research and Discoveries4 citations

TL;DR

This Festschrift volume, dedicated to Piet Groeneboom, compiles cutting-edge research in asymptotic statistics, stochastic processes, and inverse problems, reflecting his foundational contributions. It features 46 papers by leading statisticians and probabilists, covering topics from convex density estimation and empirical processes to extreme value theory and stochastic growth models, with rigorous theoretical results and novel asymptotic analyses.

ABSTRACT

In September 2006, Piet Groeneboom officially retired as professor of statistics at Delft University of Technology and the Vrije Universiteit in Amsterdam. He did so by delivering his farewell lecture `Summa Cogitatio' ([42] in Piet's publication list) in the Aula of the university in Delft. To celebrate Piet's impressive contributions to statistics and probability, the workshop `Asymptotics: particles, processes and inverse problems' was held from July 10 until July 14, 2006, at the Lorentz Center in Leiden. Many leading researchers in the fields of probability and statistics gave talks at this workshop, and it became a memorable event for all who attended, including the organizers and Piet himself. This volume serves as a Festschrift for Piet Groeneboom. It contains papers that were presented at the workshop as well as some other contributions, and it represents the state of the art in the areas in statistics and probability where Piet has been (and still is) most active. Furthermore, a short CV of Piet Groeneboom and a list of his publications are included.

Motivation & Objective

• To honor Piet Groeneboom's seminal contributions to mathematical statistics and probability theory.
• To compile state-of-the-art research in asymptotic statistics, stochastic processes, and inverse problems reflecting Groeneboom's core research areas.
• To provide a comprehensive overview of recent advances in nonparametric statistics, empirical processes, and stochastic modeling.
• To document the intellectual legacy of Groeneboom through invited contributions from leading researchers in his fields of expertise.
• To serve as a reference volume for researchers in statistics and probability, particularly in areas influenced by Groeneboom’s work on isotonic estimation, empirical processes, and limit theorems.

Proposed method

• Compilation of invited papers presented at the 'Asymptotics: Particles, Processes and Inverse Problems' workshop held in Leiden, 2006.
• Selection of high-impact contributions from leading researchers in statistics and probability, with a focus on topics central to Groeneboom’s research.
• Incorporation of theoretical advances in nonparametric estimation, including isotonic regression, convex density estimation, and empirical processes.
• Inclusion of foundational results on stochastic processes such as Hammersley’s process, zero-range processes, and Brownian motion embeddings.
• Use of rigorous asymptotic analysis, including Bahadur efficiency, concentration inequalities, and weak convergence results.
• Integration of contributions on inverse problems, deconvolution, and current status data, reflecting Groeneboom’s work on interval censoring and functional estimation.

Experimental results

Research questions

• RQ1 What are the key theoretical advances in asymptotic statistics and stochastic processes that reflect Piet Groeneboom’s research legacy?
• RQ2 How do recent developments in convex density estimation and isotonic regression improve estimation accuracy and convergence rates?
• RQ3 What are the limiting distributions and consistency properties of estimators in inverse problems such as deconvolution and current status data?
• RQ4 How do stochastic processes like Hammersley’s process and zero-range processes exhibit universal scaling limits and phase transitions?
• RQ5 What are the implications of new concentration inequalities and empirical process results for high-dimensional and dependent data models?

Key findings

• The volume establishes a comprehensive state-of-the-art overview of asymptotic statistics and stochastic processes, with a strong emphasis on nonparametric and semiparametric inference.
• Key results include the asymptotic normality of the L1-error of the Grenander estimator and the characterization of the invelope of integrated Brownian motion as a canonical process for convex function estimation.
• New bounds on the Bahadur efficiency of rank tests and improved oracle properties for SCAD-penalized least squares estimators are derived.
• The paper on Hammersley’s process with sources and sinks establishes a connection between particle systems and longest increasing subsequence statistics, with cube root asymptotics.
• Results on the support reduction algorithm and MLE consistency for current status data with competing risks provide new tools for survival analysis.
• Talagrand’s convex hull concentration inequality is refined, offering tighter bounds for empirical processes indexed by estimated functions.