Rigorous statistical procedures for data from dynamical systems

DOI10.1007/BF01010905zbMath0646.62109MaRDI QIDQ1104024

Publication date: 1986

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Hausdorff dimension simulations interval maps stationary processes U statistics symmetry tests rank statistics invariant densities ranking methods relative asymptotic efficiency Perron-Frobenius operators computations of regular functionals determination of dimension coefficients estimation of Grasberger-Procaccia correlation exponent hut-map dynamical systems invariant measures of dynamical systems symmetric densities

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Applications of statistics (62P99) Special processes (60K99)

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Statistical tests for deterministic effects in broad band time series ⋮ Exponential weak Bernoulli mixing for Collet-Eckmann maps ⋮ On weighted $U$-statistics for stationary processes. ⋮ Bootstrap for the sample mean and forU-statistics of mixing and near-epoch dependent processes ⋮ Change-point detection based on weighted two-sample U-statistics ⋮ Limit theorems for U-statistics of Bernoulli data ⋮ Markov Extensions, Zeta Functions, and Fredholm Theory for Piecewise Invertible Dynamical Systems ⋮ Multivariate linear and nonlinear causality tests ⋮ Kaplan-Meier V- and U-statistics ⋮ Dynamical hypothesis tests and decision theory for Gibbs distributions ⋮ Dependent multiplier bootstraps for non-degenerate $U$-statistics under mixing conditions with applications ⋮ Lindeberg theorem for Gibbs–Markov dynamics ⋮ Point process diagnostics based on weighted second-order statistics and their asymptotic properties ⋮ A Berry-Esseen bound with (almost) sharp dependence conditions ⋮ Deriving the asymptotic distribution of $U$- and $V$-statistics of dependent data using weighted empirical processes ⋮ Qualitative robustness of von Mises statistics based on strongly mixing data ⋮ Change-Point Detection Under Dependence Based on Two-Sample U-Statistics ⋮ Nonlinear dynamics delay times, and embedding windows ⋮ Komlós-Major-Tusnády approximation under dependence ⋮ Limit theorems for von Mises statistics of a measure preserving transformation ⋮ A new estimator for information dimension with standard errors and confidence intervals ⋮ A test for independence based on the correlation dimension ⋮ Asymptotic periodicity and banded chaos ⋮ Some results on the behavior and estimation of the fractal dimensions of distributions on attractors ⋮ Limit theorems for functionals of mixing processes with applications to $U$-statistics and dimension estimation ⋮ Dimension spectra for multbfractal measures with connections to nonparametric density estimation^∗ ⋮ On Weak Convergence in Dynamical Systems to Self-Similar Processes with Spectral Representation ⋮ DYNAMICAL CORRELATIONS ON RECONSTRUCTED INVARIANT DENSITIES AND THEIR EFFECT ON CORRELATION DIMENSION ESTIMATION ⋮ A central limit theorem for measurements on the logarithmic scale and its application to dimension estimates ⋮ Bahadur representation for $U$-quantiles of dependent data ⋮ Empirical processes of multidimensional systems with multiple mixing properties ⋮ A renewal approach to Markovian $U$-statistics ⋮ Sample Entropy Statistics and Testing for Order in Complex Physiological Signals ⋮ A Monte Carlo method for estimating the correlation exponent ⋮ Berry-Esseen theorems under weak dependence ⋮ Local correlation entropy ⋮ Properties of distributions and correlation integrals for generalized versions of the logistic map ⋮ TESTING FOR CHANGES IN KENDALL’S TAU ⋮ Estimation of dimension for spatially distributed data and related limit theorems ⋮ Chaotic time series analyses of epileptic seizures ⋮ Asymptotic distribution of two-sample empirical $U$-quantiles with applications to robust tests for shifts in location ⋮ $U$-processes, $U$-quantile processes and generalized linear statistics of dependent data ⋮ Ergodic theorems arising in correlation dimension estimation. ⋮ Central limit theorem and the bootstrap for $U$-statistics of strongly mixing data ⋮ Consistency of the Takens estimator for the correlation dimension ⋮ A maximum likelihood approach to correlation dimension and entropy estimation ⋮ On entropy, entropy-like quantities, and applications ⋮ Multivariate generalized linear-statistics of short range dependent data

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