1. Nonparametric statistical theory

• Lecturer: Prof. Phạm Ngọc Thanh Mai (MCF) - University Paris Sud 11, France.
• Time: 19 and 22 - 26/7/2013.

Abstract:

This course aims at providing an introduction to nonparametric statistical theory. Parametric
models provide only an approximation, often imprecise, of the underlying statistical structure.
Statistical models that explain the data in a more consistent way are often more complex: Unknown elements in these models are, in general, some functions having certain properties of
smoothness. The problem of nonparametric estimation consists in estimation, from the observations, of an unknown function belonging to a sufficiently large class of functions. In this course,
after having presented some of the most popular nonparametric models, we will dwell on how to
approximate functions because if one wants to estimate well, one has to approximate well. Then,
it will be time to tackle density estimation and nonparametric regression via various techniques
and see how to choose some tuning parameters on which the statistical procedures depend. Finally, we will see how to compute lower bounds on the minimax risk.

Plan of the course:

1. Examples of some nonparametric problems and models
2. Approximation of functions

• Lecturer: Prof. .Trần Viết Chí (MCF) - University Lille 1, France.
• Time: 29/7 to 02/8/2013

This course is a continuation of the course basic stochastic processes. The purpose is to introduce the very important notions of semi-martingale in continous time and of stochastic
differential equations. We will also study powerful tools to treat these
objects: Ito integral and Girsanov theorem.

Plan of the course:

I. Continous time processes
II. Continuous semi-martingales
III. Stochastic integral and Ito formula
IV. Stochastic differential equations
V. Girsanov theorem