Supremal Inequalities for Convex M-Estimators with Applications to Complete and Quick Convergence
Abstract
Let $$\hat{m}_{n}$$ be an $$M$$ -estimator for a parameter $$m$$ based on a sample of size $$n\in\mathbb{N}$$ . We derive exponential and polynomial upper bounds for the tail-probabilities of $$\sup_{k\geq n}|\hat{m}_{k}-m|$$ according as a boundedness- or a moment-condition is fulfilled. This enables us to derive rates of $$r$$ -complete convergence and also to show $$r$$ -qick convergence in the sense of Strasser.
Fields of Study & Subjects
Statistical Methods and Inference
Mathematical Analysis and Transform Methods
Sparse and Compressive Sensing Techniques
Publication details
- Journal / source
- Mathematical Methods of Statistics
- Publisher
- Allerton Press
- Volume
- 35
- Issue
- 1
- Pages
- 28–45
- Publication date
- 1 March 2026
- Language
- EN