Convergence rates in the central limit theorem for weighted sums of Bernoulli random fields
Open Access
- 21 December 2018
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 6 (2), 251-267
- https://doi.org/10.15559/18-vmsta121
Abstract
Moment inequalities for a class of functionals of i.i.d. random fields are proved. Then rates are derived in the central limit theorem for weighted sums of such randoms fields via an approximation by m-dependent random fields.Keywords
This publication has 19 references indexed in Scilit:
- Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examplesThe Annals of Probability, 2013
- A central limit theorem for stationary random fieldsStochastic Processes and their Applications, 2013
- Berry–Esséen bound of sample quantiles for φ-mixing random variablesJournal of Mathematical Analysis and Applications, 2012
- Rates of convergence in the CLT for linear random fieldsLithuanian Mathematical Journal, 2011
- Asymptotic normality of kernel estimates in a regression model for random fieldsJournal of Nonparametric Statistics, 2010
- Exact convergence rates in the central limit theorem for a class of martingalesBernoulli, 2007
- Normal approximation under local dependenceThe Annals of Probability, 2004
- Maximal Inequalities for Partial Sums of $\rho$-Mixing SequencesThe Annals of Probability, 1995
- Best Constants in Moment Inequalities for Linear Combinations of Independent and Exchangeable Random VariablesThe Annals of Probability, 1985
- The Accuracy of the Gaussian Approximation to the Sum of Independent VariatesTransactions of the American Mathematical Society, 1941