On Complete Convergence for Nonstationary ϕ-Mixing Random Variables

DOI10.1080/03610926.2012.725501zbMath1319.60059OpenAlexW1981905350MaRDI QIDQ5177588

Xinghui Wang, Aiting Shen, Jimin Ling

Publication date: 13 March 2015

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610926.2012.725501

zbMATH Keywords

complete convergenceBaum-Katz-type theorem\(\varphi\)-mixing random variables

Mathematics Subject Classification ID

Strong limit theorems (60F15)

Related Items (14)

The asymptotic normality of the linear weighted estimator in nonparametric regression models ⋮ The consistency and convergence rate for the nearest neighbor density estimator based on φ-mixing random samples ⋮ A note on the asymptotic properties of the estimators in a semiparametric regression model ⋮ Consistency and asymptotic normality of wavelet estimator in a nonparametric regression model ⋮ Asymptotics for the linear kernel quantile estimator ⋮ Asymptotic properties of M estimators in classical linear models with φ -mixing random errors ⋮ A note on complete convergence of weighted sums for array of rowwise AANA random variables ⋮ Exponential inequalities for sums of unbounded ϕ-mixing sequence and their applications ⋮ Complete moment convergence for arrays of rowwise \(\mathbf{\varphi}\)-mixing random variables ⋮ Equivalent conditions of complete moment and integral convergence for a class of dependent random variables ⋮ On the rates of asymptotic normality for recursive kernel density estimators under ϕ-mixing assumptions ⋮ The Berry-Esseen type bounds of the weighted estimator in a nonparametric model with linear process errors ⋮ The asymptotic properties of the estimators in a semiparametric regression model ⋮ Statistical inference for a heteroscedastic regression model with φ-mixing errors

Cites Work

• On complete convergence for weighted sums of \(\varphi \)-mixing random variables
• An invariance principle for \(\phi\)-mixing sequences
• Convergence rates and r-quick versions of the strong law for stationary mixing sequences
• Some Baum-Katz type results for \({\varphi}\)-mixing random variables with different distributions
• Convergence rates of the strong law for stationary mixing sequences
• Complete Convergence and the Law of Large Numbers
• On a Theorem of Hsu and Robbins

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