The candidate will work on the Le Cam estimation procedure in autoregressive processes driven by stationary Gaussian noise and random coefficient autoregressive processes. The relation between this methodology and recent machine learning procedures will also be discussed during the postdoctorate. Autoregressive processes are relatively common in the analysis of temporal series in insurance.

Particularly, the joint estimation of the drift parameter, variance parameter and Hurst parameter in the autoregressive process driven by the fractional Gaussian noise will be considered. This work follows recent works on the topic:

[1] A. Brouste, C. Cai and M. Kleptsyna (2014) Asymptotic properties of the MLE for the autoregressive process coefficients under stationary Gaussian noises, Mathematical Methods of Statistics, 23(2), 103-115

[2] Marius Soltane (2018) Asymptotic efficiency in the autoregressive process driven by a stationary Gaussian noise, hal-01899971.

[3] A. Brouste, C. Cai, M. Soltane and L. Wang (2020) Testing for the change of the mean-reverting parameter of an autoregressive model with stationary Gaussian noise, Statistical Inference for Stochastic Processes, 23(2), 301-318.