Bivariate symmetric statistics of long-range dependent observations

DOI10.1016/0378-3758(91)90023-8zbMath0737.62042OpenAlexW2044208900MaRDI QIDQ1176759

Murad S. Taqqu, Herold G. Dehling

Publication date: 25 June 1992

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-3758(91)90023-8

zbMATH Keywords

fractional Brownian motionsample variancelong-range dependenceRosenblatt processchi-squared testgoodness of fitU-statisticHoeffding decompositionvon Mises statisticmultiple integrationslowly varying at infinityCramer-von Mises-Smirnov testlocally bounded total variationstationary mean-zero Gaussian sequence

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Functional limit theorems; invariance principles (60F17)

Related Items (17)

Two-sample U-statistic processes for long-range dependent data ⋮ On weighted \(U\)-statistics for stationary processes. ⋮ Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series ⋮ Degenerate \(U\)- and \(V\)-statistics under ergodicity: asymptotics, bootstrap and applications in statistics ⋮ Renewal type bootstrap for increasing degree \(U\)-process of a Markov chain ⋮ Asymptotic properties of \(U\)-processes under long-range dependence ⋮ Qualitative robustness of von Mises statistics based on strongly mixing data ⋮ Continuous mapping approach to the asymptotics of \(U\)- and \(V\)-statistics ⋮ Limit theorems for nondegenerate \(U\)-statistics of continuous semimartingales ⋮ Sensitivity of the Hermite rank ⋮ How the instability of ranks under long memory affects large-sample inference ⋮ Covariances Estimation for Long-Memory Processes ⋮ Non‐Parametric Change‐Point Tests for Long‐Range Dependent Data ⋮ Empirical process of long-range dependent sequences when parameters are estimated ⋮ Robust estimation of the scale and of the autocovariance function of Gaussian short- and long-range dependent processes ⋮ Asymptotics for statistical functionals of long-memory sequences ⋮ Donsker results for the empirical process indexed by functions of locally bounded variation and applications to the smoothed empirical process

Cites Work

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• The empirical process of some long-range dependent sequences with an application to U-statistics
• Continuous functions whose level sets are orthogonal to all polynomials of a given degree
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Convergence of integrated processes of arbitrary Hermite rank

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