Student Seminar in Statistics: Nonparametric Estimation under ShapeConstraints
Spring semester 2018
General information
Lecturer  Fadoua Balabdaoui 

Assistants  Domagoj Cevid, Francesco Ortelli 
Lectures  Mon 1517 HG G 26.5 >> 
Course catalogue data  >> 
Course content
AbstractStatistical 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, kmonotonicity or logconcavity.
ObjectiveThe 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 socalled 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.
Announcements
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



Week 3 (05/03/2018)  Topic 2: Generalized isotonic regression problems



Week 4 (12/03/2018)  Topic 3: Estimation of a monotone density and a distribution function from Current Status data


Week 5 (19/03/2018)  Topic 4: Algorithms and computation in shapeconstrained problems


Week 6 (26/03/2018)  Topic 5: Estimation of a convex ROC curve


Week 7 (09/04/2018)  Topic 6: Mixtures of Exponential distributions


Week 8 (23/04/2018)  Topic 7: Shape restricted nonparametric regression using Bernstein polynomials


Week 9 (30/04/2018)  Topic 8: Consistent maximum likelihood estimation of a unimodal density using shape restrictions


Week 10 (07/05/2018)  Topic 9: Maximum Likelihood estimation of a logconcave density and its distribution function: Basic properties and uniform consistency


Week 11 (14/05/2017)  Topic 10: On asymptotics of the discrete convex LSE of a probability mass function


Week 12 (28/05/2017)  Topic 11: Estimation of a discrete probability under constraint of kmonotonicity
