Weak invariance of generalized U-statistics for nonstationary absolutely regular processes

DOI10.1016/0304-4149(90)90022-KzbMath0701.60025MaRDI QIDQ914240

Michel Harel, Madan Lal Puri

Publication date: 1990

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

zbMATH Keywords

Brownian motionstrong mixingabsolutely regularweak convergence of generalized U-statistics

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Brownian motion (60J65) Functional limit theorems; invariance principles (60F17) Nonparametric inference (62G99)

Related Items (5)

Weak convergence of weighted multivariate empirical U-statistics processes under mixing condition ⋮ A simple variance inequality for \(U\)-statistics of a Markov chain with applications ⋮ Nonparametric tests for model selection with time series data ⋮ Central limit theorem of the smoothed empirical distribution functions for asymptotically stationary absolutely regular stochastic processes ⋮ Weak convergence for rectangle-indexed weighted multivariate empirical \(U\)-statistic processes under mixing conditions

Cites Work

• Weak convergence of the U-statistic and weak invariance of the one-sample rank order statistic for Markov processes and ARMA models
• Convergence of empirical processes of mixing rv's on \([0,1\)]
• Limiting behavior of U-statistics, V-statistics, and one sample rank order statistics for nonstationary absolutely regular processes
• Limiting behavior of U-statistics for stationary, absolutely regular processes
• On Weak Convergence of Stochastic Processes with Multidimensional Time Parameter
• Some Limit Theorems for Stationary Processes
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