Title: Applications of the analysis on Wiener space to statistical inference
Joint with Luis A. Barboza, Khalifa es-Sebaiy, and Leo Neufcourt.
Abstract: Toolsfrom the analysis on Wiener space, including Wiener chaos calculus and the Malliavin calculus, were promoted historically to help develop the theory of stochastic analysis and its applications to other parts of probability and analysis. They are becoming increasingly helpful as sharp tools for the quantitative analysis of asymptotic questions. In this talk, after a brief introduction to these tools and their connections to normal approximations, we will discuss some applications to the generalized method of moments and to extensions of least-squares ideas for parametric estimation of general Gaussian sequences and processes. Illustration of our general results and practical performance are presented in the case of Ornstein-Uhlenbeck processes driven by fractional Gaussian noise. Some of the results are accompanied by demonstrably sharp normal asymptotics. We may mention some intriguing implications for partial observation situations.