Seminar on Probability and Statistics

Seminar information archive ~02/20Next seminarFuture seminars 02/21~

Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike

2022/10/21

①14:30-15:40- ②16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Estate Khmaladze (Victoria University of Wellington)
On the theory of distribution free testing of statistical hypothesis
  ①Empirical processes for discrete and continuous observations: structure, difficulties and resolution.
  ②Further testing problems: parametric regression and Markov chains. (ENGLISH)
[ Abstract ]
The concept of distribution free testing is familiar to all. Everybody, who heard about rank statistics, knows that the distribution of ranks is independent from the distribution of underlying random variables, provided this later is a continuous distribution on the real line. Everybody, who ever used classical goodness of fit tests like Kolmogorov - Smirnov test or Cram\'er-von Mises test, knows that the distribution of statistics of these tests is independent from the distribution of the underlying random variables, again, provided this distribution is a continuous distribution on the real line.

Development in subsequent decades revealed many cracks in existing theory and difficulties in extending the concept of distribution free testing to majority of interesting models. It gradually became clear that the new starting point is needed to expand the theory to these models.

In our lectures we first describe the current situation in empirical and related processes. Then we describe how the new approaches have been developed and what progress has been made.

Then we hope to show how the new approach can be naturally extended to the domain of stochastic processes, and how the important probabilistic models of the processes can be tested in distribution free way. In discrete time, results for Markov chains have been published in 2021. Extension to continuous time will be explored during the current visit to University of Tokyo.
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLScxh_wNRs3WbMUG4S3cGlGAu1ZkP4trLbc08CBrvUDO66hwNg/viewform?usp=sf_link