Complete f -moment convergence for maximum of weighted sums of martingale differences and its statistical applications
Abstract
In this paper, we study the complete f-moment convergence and complete r-th moment convergence for maximum of weighted sums of martingale differences random variables. A number of known results are extended by the results obtained in this paper. As applications of the main conclusions, we obtain the complete consistency of the estimator in the nonparametric regression model, the least squares estimator in the semiparametric regression model and the least squares estimators in the simple linear errors-in-variables regression model when errors are sequences of martingale difference, and the strong consistency of the least squares estimator in the multiple regression model with martingale difference errors. In addition, two numerical simulations were performed to verify the validity of the theoretical results. Finally, a real data analysis is given.
Fields of Study & Subjects
Probability and Risk Models
Approximation Theory and Sequence Spaces
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Journal of Statistical Computation and Simulation
- Publisher
- Informa UK Limited
- Volume
- 96
- Issue
- 8
- Pages
- 1911–1953
- Publication date
- 5 January 2026
- Language
- EN