An exponential inequality under weak dependence

DOI10.3150/bj/1145993977zbMath1126.62039OpenAlexW2081797450MaRDI QIDQ850748

Raoul S. Kallabis, Michael H. Neumann

Publication date: 6 November 2006

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bj/1145993977

zbMATH Keywords

cumulantsneural networksBernstein-type inequalityweak dependencepenalized least squaresnonparametric autoregressionBarron classes

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Inequalities; stochastic orderings (60E15) Non-Markovian processes: estimation (62M09)

Related Items (28)

Strong uniform consistency rates and asymptotic normality of conditional density estimator in the single functional index modeling for time series data ⋮ Parametric estimation in autoregressive processes under quasi-associated random errors ⋮ The method of cumulants for the normal approximation ⋮ Nonparametric relative regression for associated random variables ⋮ Block Bootstrapping for Kernel Density Estimators under ψ-Weak Dependence ⋮ Nonconventional moderate deviations theorems and exponential concentration inequalities ⋮ Probability and moment inequalities for sums of weakly dependent random variables, with applications ⋮ Hoeffding's inequality for sums of dependent random variables ⋮ Unnamed Item ⋮ Strong consistency of the stationary bootstrap under \(\psi\)-weak dependence ⋮ The \(k\)-nearest neighbors method in single index regression model for functional quasi-associated time series data ⋮ Exponential inequalities for Mann’s stochastic algorithm ⋮ Stationary bootstrap for kernel density estimators under \(\psi\)-weak dependence ⋮ A note on a maximal Bernstein inequality ⋮ Sieve maximum likelihood estimation of the spatial autoregressive Tobit model ⋮ Kiefer–Wolfowitz algorithm under quasi-associated random errors ⋮ Random central limit theorems for linear processes with weakly dependent innovations ⋮ Unnamed Item ⋮ Confidence intervals for the mean based on exponential type inequalities and empirical likelihood ⋮ Limit theorems for some skew products with mixing base maps ⋮ Estimation and simulation of conditional hazard function in the quasi-associated framework when the observations are linked via a functional single-index structure ⋮ Asymptotic Results for an M-Estimator of the Regression Function for Quasi-Associated Processes ⋮ Goodness-of-fit tests for Markovian time series models: central limit theory and bootstrap approximations ⋮ Semiparametric estimation for partially linear models with \(\psi\)-weak dependent errors ⋮ Asymptotic results for certain weak dependent variables ⋮ Complete convergence of stochastic approximation algorithm in ℝ^dunder random noises ⋮ Consistency of stochastic approximation algorithm with quasi-associated random errors ⋮ Kernel estimators of mode under \(\psi\)-weak dependence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Goodness-of-fit tests for Markovian time series models: central limit theory and bootstrap approximations
• Risk bounds for model selection via penalization
• Approximation and estimation bounds for artificial neural networks
• A new weak dependence condition and applications to moment inequalities
• Coupling for \(\tau\)-dependent sequences and applications
• Functional aggregation for nonparametric regression.
• Weak dependence beyond mixing and asymptotics for nonparametric regression
• On minimax identification of nonparametric autoregressive models
• A triangular central limit theorem under a new weak dependence condition
• A new covariance inequality and applications.
• Probability Inequalities for the Sum of Independent Random Variables
• Universal approximation bounds for superpositions of a sigmoidal function
• Minimum complexity regression estimation with weakly dependent observations
• Asymptotic Properties of Non-Linear Least Squares Estimators

This page was built for publication: An exponential inequality under weak dependence