|Thông báo lớp chuyên đề thống kê hè|
| Tên chuyên đề: Statistics for high-dimensional data
- Lý thuyết: GS Vincent Rivoirard (ĐH Paris Dauphine).
- Bài tập + thực hành: Hoàng Văn Hà (ĐH Lille 1).
- Lý thuyết: từ 25/7 đến 29/7. Mỗi ngày 3h, tổng cộng 15h lý thuyết.
- Bài tập + thực hành: dự kiến có từ 4 đến 6 buổi, mỗi buổi 2h.
Phần thực hành sẽ làm trên Matlab hoặc R.
Tóm tắt: Classical statistical methods developed during the last century were suitable when the number of observations is much larger than the number of parameters to infer. Unfortunately, many fields such as astronomy, genetics, medicine or neuroscience produce large and complex data sets, and consequently with models containing a large number of parameters for which classical tools are not adapted. This issue is often referred as the curse of dimensionality. The goal of this course is to provide most of fundamental statistical tools to face with high-dimensional data. The aim is to present the main concepts and ideas on some selected topics of high-dimensional statistics based on modern nonparametric methodologies such as multiple testing, kernel, wavelets and penalized estimators with a special focus on Lasso estimation. Theoretical aspects are motivated by applicable developments of presented methods. This course is based on lectures given in the master program from Paris Sud University (Orsay).
Tài liệu tham khảo:
- Bühlmann, Peter and van de Geer, Sara Statistics for high-dimensional data. Methods, theory and applications. Springer Series in Statistics. Springer, Heidelberg, 2011. xviii+556 pp. ISBN: 978-3-642-20191-2
- Giraud, Christophe Introduction to high-dimensional statistics. Monographs on Statistics and Applied Probability, 139. CRC Press, Boca Raton, FL, 2015. xvi+255 pp. ISBN: 978-1-4822-3794-8
- Härdle, Wolfgang Kerkyacharian, Gerard Picard, Dominique and Tsybakov, Alexander Wavelets, approximation, and statistical applications. Lecture Notes in Statistics, 129. Springer-Verlag, New York,1998. xviii+265 pp. ISBN: 0-387-98453-4
- Rivoirard Vincent and Stoltz Gilles Statistique mathématique en action. Vuibert. ISBN: : 978-2311007206