Asymptotic normality for -dependent and constrained -statistics, with applications to pattern matching in random strings and permutations

DOI10.1017/apr.2022.51arXiv2106.09401OpenAlexW4361207667MaRDI QIDQ6068845

Svante Janson

Publication date: 15 December 2023

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.09401

zbMATH Keywords

random wordsvincular patternsconstrained occurrences

Mathematics Subject Classification ID

Parametric inference (62Fxx) Permutations, words, matrices (05A05) Combinatorial probability (60C05) Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) (68Q87)

Cites Work

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• A multivariate CLT for bounded decomposable random vectors with the best known rate
• On normal approximations of distributions in terms of dependency graphs
• Convergence rates for generalized descents
• The distribution of subword counts is usually normal
• Asymptotic distributions of weighted \(U\)-statistics of degree 2
• A multivariate CLT for decomposable random vectors with finite second moments
• A central limit theorem for \(m\)-dependent random variables
• Generalized descents and normality
• Central limit theorem and the bootstrap for \(U\)-statistics of strongly mixing data
• Renewal theory for m-dependent variables
• Symmetric statistics, Poisson point processes, and multiple Wiener integrals
• Limit theorems for a triangular scheme of U-statistics with applications to inter-point distances
• Normal convergence by higher semi-invariants with applications to sums of dependent random variables and random graphs
• Asymptotic distribution of symmetric statistics
• Asymptotic normality of permutation statistics derived from weighted sums of bivariate functions
• A central limit theorem for decomposable random variables with applications to random graphs
• On pattern frequency occurrences in a Markovian sequence
• Asymptotic distributions for weighted \(U\)-statistics
• On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted \(U\)-statistics
• Weak convergence of generalized U-statistics
• Renewal theory for asymmetric \(U\)-statistics
• On inference validity of weighted U-statistics under data heterogeneity
• Motif statistics.
• On weighted \(U\)-statistics for stationary processes.
• On normal approximation rates for certain sums of dependent random variables
• On the asymptotic normality of sequences of weak dependent random variables
• Hidden words statistics for large patterns
• On the asymptotic statistics of the number of occurrences of multiple permutation patterns
• Inference of weighted \(V\)-statistics for nonstationary time series and its applications
• Patterns in random permutations
• Spectral analysis of word statistics
• On degenerate sums of m-dependent variables
• On Three Different Notions of Monotone Subsequences
• The Invariance Principle for Dependent Random Variables
• Pattern Matching Statistics on Correlated Sources
• Stopped Random Walks
• Hidden word statistics
• Normal Approximation by Stein’s Method
• On Some Convergence Properties of UStatistics
• Nonparametric Measures of Angular-Angular Association
• Limiting behavior of U-statistics for stationary, absolutely regular processes
• Some properties of incomplete U-statistics
• Gaussian Hilbert Spaces
• A Central Limit Theorem for Vincular Permutation Patterns
• A Refinement of the Central Limit Theorem forU-Statistics ofm-Dependent Variables
• Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions
• Limiting behavior of regular functionals of empirical distributions for stationary *-mixing processes
• On the Properties of U-Statistics when the Observations are not Independent
• A Class of Statistics with Asymptotically Normal Distribution
• Transformations of Wiener Integrals Under a General Class of Linear Transformations
• Probability: A Graduate Course
• The number of occurrences of patterns in a random tree or forest permutation

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