Some upper bounds for the rate of convergence of penalized likelihood context tree estimators
Florencia Leonardi
Abstract
We find upper bounds for the probability of underestimation and overestimation errors in penalized likelihood context tree estimation. The bounds are explicit and applies to processes of not necessarily finite memory. We allow for general penalizing terms and we give conditions over the maximal depth of the estimated trees in order to get strongly consistent estimates. This generalizes previous results obtained in the case of estimation of the order of a Markov chain.
Create a lesson
Related papers
Instance-Optimal Adaptive Location Estimation via Multiscale Mid-Summaries
Qiaosen Wang, Chao Gao
Robust Multi-Task Learning for Principal Component Analysis
Dali Liu, Haolei Weng
Principal component error in high-dimensional factor models
Alex Bernstein, Lisa R. Goldberg, Nicholas Gunther et al.
Approximation Theorems for High-Dimensional Canonical U-Statistics: Gaussian Chaos and Phase Transition
Leheng Cai, Qirui Hu
On the parametric and semiparametric Fisher information matrix for non-zero mean stationary spherical invariant random processes
Jean-Pierre Delmas, Habti Abeida, Stefano Fortunati
Inference for two-stage sampling in spatial surveys
Guillaume Chauvet, Olivier Bouriaud, Trinh H. K. Duong