Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/11262
Title: | Convergence rates for the strong law of large numbers under association | Authors: | Henriques, Carla Oliveira, Paulo Eduardo |
Keywords: | Association; Convergence rates; Exponential inequalities; Maximal inequalities | Issue Date: | 2008 | Publisher: | Centro de Matemática da Universidade de Coimbra | Citation: | Pré-Publicações DMUC. 08-14 (2008) | Abstract: | We prove convergence rates for the Strong Laws of Large Numbers (SLLN) for associated variables which are arbitrarily close to the optimal rates for independent variables. A rst approach is based on exponential inequalities, a usual tool for this kind of problems. Following the optimization e orts of several authors, we improve the rates derived from exponential inequalities to log2 n n1=2 . A more recent approach tries to use maximal inequalities together with moment inequalities. We prove a new maximal order inequality of order 4 for associated variables, using a telescoping argument. This inequality is then used to prove a SLLN convergence rate arbitrarily close to log1=4 n n1=2 . | URI: | https://hdl.handle.net/10316/11262 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Convergence rates for the strong law.pdf | 154.7 kB | Adobe PDF | View/Open |
Page view(s)
264
checked on Aug 13, 2024
Download(s)
79
checked on Aug 13, 2024
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.