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<p>As a key branch of probability theory and mathematical statistics, probability limit theory focuses on analyzing the convergence properties of random variable sequences and their associated distribution functions. Complete <i>f</i>-moment convergence is much general than complete convergence and complete moment convergence. In this paper, we study the complete <i>f</i>-moment convergence for rowwise <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(m_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>m</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>-extended negatively dependent random variables, which is a new dependence structure. The results on complete <i>f</i>-moment convergence are obtained under some suitable conditions, which generalize the corresponding ones in the literature. As an application, we establish the complete consistency for the G-M estimator of nonparametric regression models. Moreover, a series of simulations are implemented to show the numerical performance of theoretical results based on finite samples.</p>

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Complete f-Moment Convergence for Arrays of Rowwise \(m_{n}\)-Extended Negatively Dependent Random Variables and its Application

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Yanjiang Chen,
  • Andrei Volodin,
  • Xuejun Wang

摘要

As a key branch of probability theory and mathematical statistics, probability limit theory focuses on analyzing the convergence properties of random variable sequences and their associated distribution functions. Complete f-moment convergence is much general than complete convergence and complete moment convergence. In this paper, we study the complete f-moment convergence for rowwise \(m_n\) m n -extended negatively dependent random variables, which is a new dependence structure. The results on complete f-moment convergence are obtained under some suitable conditions, which generalize the corresponding ones in the literature. As an application, we establish the complete consistency for the G-M estimator of nonparametric regression models. Moreover, a series of simulations are implemented to show the numerical performance of theoretical results based on finite samples.