# 401-3620-20L  Student Seminar in Statistics: Inference in Non-Classical Regression Models

 Semester Frühjahrssemester 2021 Dozierende F. Balabdaoui Periodizität einmalige Veranstaltung Lehrveranstaltung Findet dieses Semester nicht statt. Lehrsprache Englisch Kommentar Maximale Teilnehmerzahl: 24Hauptsächlich für Studierende der Bachelor- und Master-Studiengänge Mathematik, welche nach der einführenden Lerneinheit 401-2604-00L Wahrscheinlichkeit und Statistik (Probability and Statistics) mindestens ein Kernfach oder Wahlfach in Statistik besucht haben. Das Seminar wird auch für Studierende der Master-Studiengänge Statistik bzw. Data Science angeboten.

 Kurzbeschreibung Review of some non-standard regression models and the statistical properties of estimation methods in such models. Lernziel The main goal is the students get to discover some less known regression models which either generalize the well-known linear model (for example monotone regression) or violate some of the most fundamental assumptions (as in shuffled or unlinked regression models). Inhalt Linear regression is one of the most used models for prediction and hence one of the most understood in statistical literature. However, linearity might too simplistic to capture the actual relationship between some response and given covariates. Also, there are many real data problems where linearity is plausible but the actual pairing between the observed covariates and responses is completely lost or at partially. In this seminar, we review some of the non-classical regression models and the statistical properties of the estimation methods considered by well-known statisticians and machine learners. This will encompass:1. Monotone regression2. Single index model3. Unlinked regression4. Partially unlinked regression Skript No script is necessary for this seminar Literatur In the following is the material that will read and studied by each pair of students (all the items listed below are available through the ETH electronic library or arXiv):1. Chapter 2 from the book "Nonparametric estimation under shape constraints" by P. Groeneboom and G. Jongbloed, 2014, Cambridge University Press2. "Nonparametric shape-restricted regression" by A. Guntuoyina and B. Sen, 2018, Statistical Science, Volume 33, 568-5943. "Asymptotic distributions for two estimators of the single index model" by Y. Xia, 2006, Econometric Theory, Volume 22, 1112-1137 4. "Least squares estimation in the monotone single index model" by F. Balabdaoui, C. Durot and H. K. Jankowski, Journal of Bernoulli, 2019, Volume 4B, 3276-33105. "Least angle regression" by B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, 2004, Annals of Statsitics, Volume 32, 407-499.6. "Sharp thresholds for high dimensional and noisy sparsity recovery using l1-constrained quadratic programming (Lasso)" by M. Wainwright, 2009, IEEE transactions in Information Theory, Volume 55, 1-197."Denoising linear models with permuted data" by A. Pananjady, M. Wainwright and T. A. Courtade and , 2017, IEEE International Symposium on Information Theory, 446-450.8. "Linear regression with shuffled data: statistical and computation limits of permutation recovery" by A. Pananjady, M. Wainwright and T. A. Courtade , 2018, IEEE transactions in Information Theory, Volume 64, 3286-33009. "Linear regression without correspondence" by D. Hsu, K. Shi and X. Sun, 2017, NIPS10. "A pseudo-likelihood approach to linear regression with partially shuffled data" by M. Slawski, G. Diao, E. Ben-David, 2019, arXiv.11. "Uncoupled isotonic regression via minimum Wasserstein deconvolution" by P. Rigollet and J. Weed, 2019, Information and Inference, Volume 00, 1-27