Student Seminar in Statistics: Nonparametric Estimation under Shape-Constraints

Spring semester 2018

General information

Lecturer Fadoua Balabdaoui
Assistants Domagoj Cevid, Francesco Ortelli
Lectures Mon 15-17 HG G 26.5 >>
Course catalogue data >>

Course content


Statistical inference based on a random sample can be performed under additional shape restrictions on the unknown entity to be estimated (regression curve, probability density,...). Under shape restrictions, we mean a variety of constraints. Examples thereof include monotonicity, bounded variation, convexity, k-monotonicity or log-concavity.


The main goal of this Student Seminar is to get acquainted with the existing approaches in shape constrained estimation. The students will get to learn that specific estimation techniques can be used under shape restrictions to obtain better estimators, especially for small/moderate sample sizes. Students will also have the opportunity to learn that one of the main merits of shape constrained inference is to avoid choosing some arbitrary tuning parameter as it is the case with bandwidth selection in kernel estimation methods. Furthemore, students will get to read about some efficient algorithms that can be used to fastly compute the obtained estimators. One of the famous algoritms is the so-called PAVA (Pool Adjacent Violators Algorithm) used under monotonicity to compute a regression curve or a probability density. During the Seminar, the students will have to study some selected chapters from the book "Statistical Inference under Order Restrictions" by Barlow, Bartholomew, Bremner and Brunk as well as some "famous" articles on the subject.


Course materials

Week Topic Material Students' Slides
Week 1 (19/02/2018) Introduction / Assignment of the topics.
Week 2 (26/02/2018) Topic 1: Isotonic Regression
  • Students: Simon Gubler, Tinatin Mamageishvili
  • Assistant: Domagoj Cevid
  • Ch. 1.2 and part of Ch. 1.3 from BBBB
  • pp. 5-30
Week 3 (05/03/2018) Topic 2: Generalized isotonic regression problems
  • Students: Corinne Emmenegger, Florian Krach
  • Assistant: Francesco Ortelli
  • Ch. 1.4 and part of Ch. 1.5 from BBBB
  • p.38-53
Week 4 (12/03/2018) Topic 3: Estimation of a monotone density and a distribution function from Current Status data
  • Students: Cédric Bleuler, Partick Gantner
  • Assistant: Francesco Ortelli
Week 5 (19/03/2018) Topic 4: Algorithms and computation in shape-constrained problems
  • Students: Casimir Fürer, Johannes Ladwig
  • Assistant: Domagoj Cevid
Week 6 (26/03/2018) Topic 5: Estimation of a convex ROC curve
  • Students: Ramon Braunwarth, Marc Netzer
  • Assistant: Domagoj Cevid
Week 7 (09/04/2018) Topic 6: Mixtures of Exponential distributions
  • Students: Isaia Albisetti, Sanzio Monti
  • Assistant: Francesco Ortelli
Week 8 (23/04/2018) Topic 7: Shape restricted nonparametric regression using Bernstein polynomials
  • Students: Leon Carl, Danting Wu
  • Assistant: Domagoj Cevid
Week 9 (30/04/2018) Topic 8: Consistent maximum likelihood estimation of a unimodal density using shape restrictions
  • Students: Camilla Gerboth, Lilian Müller
  • Assistant: Domagoj Cevid
Week 10 (07/05/2018) Topic 9: Maximum Likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency
  • Students: Yll Haziri, Claudio Orellano
  • Assistant: Francesco Ortelli
Week 11 (14/05/2017) Topic 10: On asymptotics of the discrete convex LSE of a probability mass function
  • Students: Rinaldo Caranzano, Cecilia Lombardi
  • Assistant: Francesco Ortelli
Week 12 (28/05/2017) Topic 11: Estimation of a discrete probability under constraint of k-monotonicity
  • Students: Pietro Cattaneo, David Inauen
  • Assistants: Francesco Ortelli