# 401-3620-20L Student Seminar in Statistics: Inference in Some Non-Standard Regression Problems

Semester | Autumn Semester 2021 |

Lecturers | F. Balabdaoui |

Periodicity | every semester recurring course |

Language of instruction | English |

Comment | Number of participants limited to 24. Mainly for students from the Mathematics Bachelor and Master Programmes who, in addition to the introductory course unit 401-2604-00L Probability and Statistics, have heard at least one core or elective course in statistics. Also offered in the Master Programmes Statistics resp. Data Science. |

### Courses

Number | Title | Hours | Lecturers | ||||
---|---|---|---|---|---|---|---|

401-3620-00 S | Student Seminar in Statistics: Inference in Some Non-Standard Regression Problems Remark: former title in FS 2020: Student Seminar in Statistics: Inference in Non-Classical Regression Models | 2 hrs |
| F. Balabdaoui |

### Catalogue data

Abstract | Review of some non-standard regression models and the statistical properties of estimation methods in such models. |

Learning objective | 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). |

Content | Linear regression is one of the most used models for prediction and hence one of the most understood in statistical literature. However, linearity might be 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 regression 2. Single index model 3. Unlinked regression |

Literature | In the following is the tentative material that will be read and studied by each pair of students (all the items listed below are available through the ETH electronic library or arXiv). Some of the items might change. 1. Chapter 2 from the book "Nonparametric estimation under shape constraints" by P. Groeneboom and G. Jongbloed, 2014, Cambridge University Press 2. "Nonparametric shape-restricted regression" by A. Guntuoyina and B. Sen, 2018, Statistical Science, Volume 33, 568-594 3. "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, 3276-3310 5. "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, 1-19 7."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, 3286-3300 9. "Linear regression without correspondence" by D. Hsu, K. Shi and X. Sun, 2017, NIPS 10. "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 |

Prerequisites / Notice | The students need to be comfortable with regression models, classical estimation methods (Least squares, Maximum Likelihood estimation...), rates of convergence, asymptotic normality, etc. |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 4 credits |

Examiners | F. Balabdaoui |

Type | ungraded semester performance |

Language of examination | English |

Repetition | Repetition only possible after re-enrolling for the course unit. |

Admission requirement | Not for students who already registered for this seminar (course unit 401-3620-20L) in the Spring Semester 2020. |

### Learning materials

No public learning materials available. | |

Only public learning materials are listed. |

### Groups

No information on groups available. |

### Restrictions

Places | Limited number of places. Special selection procedure. |

Beginning of registration period | Registration possible from 02.08.2021 |

Priority | Registration for the course unit is until 29.08.2021 only possible for the primary target group |

Primary target group | Data Science MSc (261000)
Mathematics BSc (404000) starting semester 05 Statistics MSc (436000) Mathematics MSc (437000) Applied Mathematics MSc (437100) Mathematics (Mobility) (448000) |

Waiting list | until 27.09.2021 |

End of registration period | Registration only possible until 17.09.2021 |

### Offered in

Programme | Section | Type | |
---|---|---|---|

Data Science Master | Seminar | W | |

Mathematics Bachelor | Seminars | W | |

Mathematics Master | Seminars | W | |

Statistics Master | Seminar or Semester Paper | W |