Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions

Abstract

This is an update of, and a supplement to, a 1986 survey paper by the author on basic properties of strong mixing conditions.

Published at http://dx.doi.org/10.1214/154957805100000104 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Cited by in corpus (186)

• PCA consistency in high dimension, low sample size context
• Extremes and Recurrence in Dynamical Systems
• Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators Under Weak Dependence and Weak Conditions
• Universal Estimation of Directed Information
• Extremal Index, Hitting Time Statistics and periodicity
• A Direct Estimation of High Dimensional Stationary Vector Autoregressions
• Random Matrices with Slow Correlation Decay
• Efficient estimation of copula-based semiparametric Markov models
• Tests alternative to higher criticism for high-dimensional means under sparsity and column-wise dependence
• Convergence to Lévy stable processes under some weak dependence conditions
• Robust empirical mean Estimators
• Second-Order Coding Rates for Channels with State
• The Multivariate Hawkes Process in High Dimensions: Beyond Mutual Excitation
• Deriving the asymptotic distribution of U- and V-statistics of dependent data using weighted empirical processes
• A Kernel Independence Test for Random Processes
• Propagation of Memory Parameter from Durations to Counts
• Variance bounding Markov chains
• Rank Determination in Tensor Factor Model
• Limit theorems for stationary Markov processes with L2-spectral gap
• Separation of the largest eigenvalues in eigenanalysis of genotype data from discrete subpopulations
• Parametric and nonparametric models and methods in financial econometrics
• Central limit theorems for high dimensional dependent data
• Consensus over Random Graph Processes: Network Borel-Cantelli Lemmas for Almost Sure Convergence
• Typical support and Sanov large deviations of correlated states
• A Wild Bootstrap for Degenerate Kernel Tests
• The notion of $\psi$-weak dependence and its applications to bootstrapping time series
• Robust estimation and inference for heavy tailed GARCH
• Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise
• On the Information Dimension of Multivariate Gaussian Processes
• On the Information Dimension of Stochastic Processes
• Estimating beta-mixing coefficients via histograms
• Superdiffusive limits for deterministic fast-slow dynamical systems
• Intermittency of Superpositions of Ornstein-Uhlenbeck Type Processes
• Predictive PAC Learning and Process Decompositions
• Clustering processes
• Statistical Inference of the Value Function for Reinforcement Learning in Infinite Horizon Settings
• The weak Bernoulli property for matrix Gibbs states
• On the computation of the extremal index for time series
• Obtaining Measure Concentration from Markov Contraction
• The tail process and tail measure of continuous time regularly varying stochastic processes
• Optimal covariance matrix estimation for high-dimensional noise in high-frequency data
• Ergodicity and mixing bounds for the Fisher-Snedecor diffusion
• Consistent Causal Inference from Time Series with PC Algorithm and its Time-Aware Extension
• The Slepian zero set, and Brownian bridge embedded in Brownian motion by a spacetime shift
• Greedy algorithms for prediction
• Interference in disordered systems: A particle in a complex random landscape
• Qualitative robustness of statistical functionals under strong mixing
• Queue-reactive Hawkes models for the order flow
• On limit theorems for continued fractions
• Change Detection of Markov Kernels with Unknown Pre and Post Change Kernel
• Asymptotic properties of estimators in a stable Cox-Ingersoll-Ross model
• Asymptotic results for sample autocovariance functions and extremes of integrated generalized Ornstein-Uhlenbeck processes
• Szegö's Theorem and its Probabilistic Descendants
• A local limit theorem for a transient chaotic walk in a frozen environment
• Does the Markov Decision Process Fit the Data: Testing for the Markov Property in Sequential Decision Making
• On $\alpha$-covariance, long, short and negative memories for sequences of random variables with infinite variance
• Partial sums of biased random multiplicative functions
• Generalization error bounds for stationary autoregressive models
• Matching of observations of dynamical systems, with applications to sequence matching
• Forecasting time series with encoder-decoder neural networks
• Recurrence times, waiting times and universal entropy production estimators
• Strong laws of large number for intermediately trimmed Birkhoff sums of observables with infinite mean
• Non-regular g-measures and variable length memory chains
• A Statistical Investigation of Long Memory in Language and Music
• Metric and Mixing Sufficient Conditions for Concentration of Measure
• Statistical analysis of Wasserstein GANs with applications to time series forecasting
• Deeply-Debiased Off-Policy Interval Estimation
• Mixing it up: A general framework for Markovian statistics
• Dimensionality Reduction for Stationary Time Series via Stochastic Nonconvex Optimization
• A bound of the $\beta$-mixing coefficient for point processes in terms of their intensity functions
• Pseudo-variance quasi-maximum likelihood estimation of semi-parametric time series models
• High-Rate Vector Quantization for the Neyman-Pearson Detection of Correlated Processes
• Mean convergence for intermediately trimmed Birkhoff sums of observables with regularly varying tails
• Estimating the Mixing Time of Ergodic Markov Chains
• Dependency-dependent Bounds for Sums of Dependent Random Variables
• Stein Self-Repulsive Dynamics: Benefits From Past Samples
• Empirical measures and random walks on compact spaces in the quadratic Wasserstein metric
• Estimation of Zero Intelligence Models by L1 Data
• Parametric Estimation from Approximate Data: Non-Gaussian Diffusions
• Sequential causal inference in a single world of connected units
• Learning from dependent observations
• Second-Order Coding Rates for Conditional Rate-Distortion
• Probability inequalities for high dimensional time series under a triangular array framework
• On Empirical Risk Minimization with Dependent and Heavy-Tailed Data
• A Survey of Estimation Methods for Sparse High-dimensional Time Series Models
• On a waiting-time result of Kontoyiannis: mixing or decoupling?
• A new CLT for additive functionals of Markov chains
• A Bernstein Inequality For Spatial Lattice Processes
• A Kernel Test for Three-Variable Interactions with Random Processes
• Conditional Risk Minimization for Stochastic Processes
• Moderate deviations in random graphs and Bernoulli random matrices
• Kernel Autocovariance Operators of Stationary Processes: Estimation and Convergence
• A General Framework for Prediction in Time Series Models
• Projected State-action Balancing Weights for Offline Reinforcement Learning
• Potential well in Poincaré recurrence
• Equidistribution of continued fraction convergents in $\mathrm{SL}(2,{\mathbb{Z}}_m)$ with an application to local discrepancy
• A Strong Law of Large Numbers for Strongly Mixing Processes
• Large deviations of return times and related entropy estimators on shift spaces
• On the continued fraction expansion of absolutely normal numbers
• Learning from networked examples
• Universal Compressed Sensing
• Limit theorems for invariant distributions
• Learning from networked examples in a k-partite graph
• Normal approximation for associated point processes via Stein's method with applications to determinantal point processes
• The complete $L^q$-spectrum and large deviations for return times for equilibrium states with summable potentials
• Trimmed sums for observables on the doubling map
• Nuisance Parameters Free Changepoint Detection in Non-stationary Series
• Learning theory estimates with observations from general stationary stochastic processes
• On the Ziv-Merhav theorem beyond Markovianity
• On the central limit theorem for unsharp quantum random variables
• Limiting distributions for explosive PAR(1) time series with strongly mixing innovation
• Statistical inference for heavy tailed series with extremal independence
• Model-Free Change Point Detection for Mixing Processes
• A CLT for dependent random variables, with an application to an infinite system of interacting diffusion processes
• A Simple Online Parameter Estimation Technique with Asymptotic Guarantees
• Nyström Regularization for Time Series Forecasting
• A Pooled Quantile Estimator for Parallel Simulations
• Regularized Nonlinear Regression with Dependent Errors and its Application to a Biomechanical Model
• Equivalence-Singularity Dichotomy in Markov Measures
• Hammersley's harness process: invariant distributions and height fluctuations
• A Geospatial Functional Model For OCO-2 Data with Application on Imputation and Land Fraction Estimation
• Adaptive Sequential Design for a Single Time-Series
• Extreme Eigenvalues of Nonlinear Correlation Matrices with Applications to Additive Models
• Consistent Entropy Estimation for Stationary Time Series
• False discovery rate control under reduced precision computation for analysis of neuroimaging data
• Quenched large deviations of Birkhoff sums along random quantum measurements
• Adaptive Reference-Guided Estimation of Principal Component Subspace in High Dimensions
• Limit theorems for counting large continued fraction digits
• Change-Point Detection for Object-valued Time Series
• Whittle estimation based on the extremal spectral density of a heavy-tailed random field
• Long range dependence and the dynamics of exploited fish populations
• On the Growth of a Ballistic Deposition Model on Finite Graphs
• Construction and Analysis of Posterior Matching in Arbitrary Dimensions via Optimal Transport
• Robust change point tests by bounded transformations
• A vector-valued almost sure invariance principle for Sinai billiards with random scatterers
• Faster Functional Clustering via Gaussian Mixture Models
• An Exponential Inequality for U-Statistics under Mixing Conditions
• Statistical Inference on Panel Data Models: A Kernel Ridge Regression Method
• Oracle approach and slope heuristic in context tree estimation
• The Generalization Ability of Online Algorithms for Dependent Data
• Ergodic Mirror Descent
• Learning Parametric-Output HMMs with Two Aliased States
• PAC-Bayes Bounds on Variational Tempered Posteriors for Markov Models
• Number of visits in arbitrary sets for $\varphi$-mixing dynamics
• Kalman Filtering over Fading Channels: Zero-One Laws and Almost Sure Stabilities
• The $\beta$-Delaunay tessellation IV: Mixing properties and central limit theorems
• Almost sure limit theorems with applications to non-regular continued fraction algorithms
• Characterization of the stability of chains associated with $g$-measures
• On the asymptotics of extremal lp-blocks cluster inference
• Discrete Time Harness Processes
• Offline Estimation of Controlled Markov Chains: Minimaxity and Sample Complexity
• Factor Models for High-Dimensional Functional Time Series
• Almost sure recovery in quasi-periodic structures
• Changepoint in Linear Relations
• On a Generalization of the Average Distance Classifier
• Renewal model for dependent binary sequences
• Monte Carlo Quantum Computing
• A Multivariate Functional Limit Theorem in Weak M1 Topology
• Extremal behavior of pMAX processes
• Joint FCLT for Sample Quantile and Measures of Dispersion for Functionals of Mixing Processes
• Limit Theorems in Hidden Markov Models
• On Selecting Stable Predictors in Time Series Models
• Posterior consistency for the spectral density of non-Gaussian stationary time series
• Totally ergodic generalised matrix equilibrium states have the Bernoulli property
• Strong mixing properties of max-infinitely divisible random fields
• Weak convergence of multivariate partial maxima processes
• Digital double barrier options: Several barrier periods and structure floors
• Latent Model Extreme Value Index Estimation
• Convergence of persistence diagrams for discrete time stationary processes
• Ziv-Merhav estimation for hidden-Markov processes
• Estimation of the transition density of a Markov chain
• Nonparametric Quantile Regression for Homogeneity Pursuit in Panel Data Models
• Conditional Extreme Value Estimation for Dependent Time Series
• Autoregressive Process Modeling via the Lasso Procedure
• Repetition and recurrence times: Dual statements and summable mixing rates
• On Validating Angular Power Spectral Models for the Stochastic Gravitational-Wave Background Without Distributional Assumptions
• A model specification test for the variance function in nonparametric regression
• Retrospective change-point detection and estimation in multivariate linear models
• A Sliding Blocks Estimator for the Extremal Index
• Large jumps of $q$-Ornstein-Uhlenbeck processes
• Ordinal Patterns Based Testing of Spatial Independence in Irregular Spatial Structures
• Scaling limits of discrete copulas are bridged Brownian sheets
• A physical study of the LLL algorithm
• Pseudo-Random Fluctuations, Stochastic Cooperativity and Burstiness in Dynamically Unstable High-Dimensional Biochemical Networks
• Uniform Risk Bounds for Learning with Dependent Data Sequences
• A central limit theorem for the variation of the sum of digits