par Fischer, Adrian 
Président du jury Alonso Garcia, Jennifer
Promoteur Swan, Yvik
Publication Non publié, 2023-10-02
Président du jury Alonso Garcia, Jennifer
Promoteur Swan, Yvik
Publication Non publié, 2023-10-02
Thèse de doctorat
| Résumé : | This thesis can be divided into two parts. In the first part (Chapter 2) we apply Stein's method in the classical sense to the normal approximation of the posterior distribution in exponential families. In Bayesian statistics it is well known that the normalised posterior distribution approaches the standard normal distribution as the sample size grows. We work out bounds on the total variation and Wasserstein distance between the standardised posterior and the standard normal distribution in the case where likelihood of the data comes from an exponential family and apply these general bounds to several examples of exponential families. In the second part (Chapter 3 and Chapter 4) we leave classical Stein's method behind and use Stein operators together with a appropriate function classes for the purpose of parameter estimation. We develop a new class of moment-type point estimators for univariate ergodic and strictly stationary time series and establish consistency as well as asymptotic normality. Moreover, we obtain a two-step estimator which reaches asymptotic effciency. The new estimators are then compared to methods from the literature through simulation studies for several examples. |
