Theory of U-Statistics and their applications is a set of lectures within Mathematics for daTa scieNce study plan

Anand N. Vidyashankar

Anand N. Vidyashankar
(George Mason University)
Personal website
Bio Anand Vidyashankar's primary research interests involve biostatistics, statistics, and biotechnology, statistical models for the Internet, statistics in finance, data confidentiality, probability, and stochastic processes. The National Science Foundation and industry partners support his research.

Prerequisites

  • Probability
  • Statistical Inference

Aim

These set of lectures provide an introduction to the ideas and methods of U-statistics

Syllabus

The theory of U-statistics goes back to the fundamental work of Hoeffding, in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated “algebraically” than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U-statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The course will cover main results such as law of large numbers, central limit theorems and law of iterated logarithms with applications in non-parametric statistics and machine learning problems.

References

  • korolyuk, V.S. and Borovskich, Y.V. (2013) Theory of U-Statistics
  • Lee, A.J. (1990) U-statistics: Theory and Practice

Schedule

  • 2021/10/22 9.30-11.30, Room A209 @ Povo 1
  • 2021/10/29 9.30-11.30, Room A209 @ Povo 1
  • 2021/11/05 9.30-11.30, Room A209 @ Povo 1
  • 2021/11/12 9.30-11.30, Room Seminari -1 @ Povo 0
  • 2021/11/19 9.30-11.30, Room A209 @ Povo 1
  • 2021/11/26 9.30-11.30, Room A209 @ Povo 1
  • 2021/12/03 9.30-11.30, Room A209 @ Povo 1
  • 2021/12/07 16.30-18.30, Room A222 @ Povo 1
  • 2021/12/10 9.30-11.30, Room A209 @ Povo 1

Details

  • Venue: Polo Scientifico e Tecnologico F. Ferrari
  • Language: English
  • The participation is free. Please send an email to Prof. Claudio Agostinelli. This is important to book the approrpiate room.
  • For further information, please contact Prof. Claudio Agostinelli

Material (Restricted access, user: US2021)

Note

Video