Weak convergence for smooth estimator of a distribution function under negative association

DOI10.1080/07362999908809595zbMath0927.62031OpenAlexW2013247744MaRDI QIDQ4237951

George G. Roussas, Zong-Wu Cai

Publication date: 14 December 1999

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362999908809595

zbMATH Keywords

weak convergencetightnessstationaritynegative associationsmooth estimate

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05)

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A nonclassical law of the iterated logarithm for functions of positively associated random variables, Smooth estimate of quantiles under association, Tightness criterion and weak convergence for the generalized empirical process in \(D[0, 1\)], Spatial local M-estimation under association, Asymptotic normality of the kernel estimate of a probability density function under association

Cites Work

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• Independence via uncorrelatedness under certain dependence structures
• A Berry-Esséen theorem and a functional law of the iterated logarithm for weakly associated random vectors
• Normal fluctuations and the FKG inequalities
• Uniform strong estimation under \(\alpha\)-mixing, with rates
• A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences
• Negative association of random variables, with applications
• Asymptotic normality of a smooth estimate of a random field distribution function under association
• Smoothing parameter selection for smooth distribution functions
• Smooth estimators of distribution and density functions
• Relative efficiency and deficiency of kernel type estimators of smooth distribution functions
• Efficient Estimation of a Distribution Function under Quadrant Dependence
• Strong uniform consistency of integrals of density estimators
• Convergence rate of perturbed empirical distribution functions
• Some Concepts of Dependence
• Some New Estimates for Distribution Functions
• Nonparametric Estimation of the Transition Distribution Function of a Markov Process
• Dependence and Aging Aspects of Multivariate Survival
• Weak convergence of probability measures and random functions in the function space D[0,∞)
• Convergence of stochastic processes