Functional convergence of sequential \(U\)-processes with size-dependent kernels
DOI10.1214/21-AAP1688zbMath1485.60037arXiv1912.02705OpenAlexW3092083555MaRDI QIDQ2117455
Mikołaj J. Kasprzak, Giovanni Peccati, Christian Döbler
Publication date: 21 March 2022
Published in: The Annals of Applied Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1912.02705
functional limit theoremsStein's method\(U\)-statisticsrandom geometric graphsasymptotic properties of estimatorsproduct formulaeHoeffding decompositionsconstractions
Asymptotic properties of nonparametric inference (62G20) Geometric probability and stochastic geometry (60D05) Functional limit theorems; invariance principles (60F17)
Related Items (2)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stochastic analysis for Poisson point processes. Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry
- Asymptotic normality of quadratic estimators
- Quantitative de Jong theorems in any dimension
- U-processes: Rates of convergence
- Limit theorems for \(U\)-processes
- Invariance principle for symmetric statistics
- A central limit theorem for generalized multilinear forms
- A functional combinatorial central limit theorem
- Symmetric statistics, Poisson point processes, and multiple Wiener integrals
- Limit theorems for a triangular scheme of U-statistics with applications to inter-point distances
- Invariance principles for changepoint problems
- Stein's method for diffusion approximations
- On the invariance principle for U-statistics
- Applications of ANOVA type decompositions for comparisons of conditional variance statistics including jackknife estimates
- Covariances of symmetric statistics
- A class of \(U\)-statistics and asymptotic normality of the number of \(k\)- clusters
- Functional limit theorems for U-statistics in the degenerate case
- Functional limit theorems for random multilinear forms
- An extension of the Csörgő-Horváth functional limit theorem and its applications to changepoint problems
- Estimation of integral functionals of a density and its derivatives
- Quantitative CLTs for symmetric \(U\)-statistics using contractions
- Renewal theory for asymmetric \(U\)-statistics
- Asymptotic distribution-free change-point detection for multivariate and non-Euclidean data
- Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications
- On the uniqueness of maximizers of Markov-Gaussian processes
- Efficient estimation of integral functionals of a density
- Adaptive estimation of a quadratic functional by model selection.
- On the estimation of multiple random integrals and \(U\)-statistics
- Jackknife multiplier bootstrap: finite sample approximations to the \(U\)-process supremum with applications
- Stein's method for multivariate Brownian approximations of sums under dependence
- Convergence of \(U\)-processes in Hölder spaces with application to robust detection of a changed segment
- The functional Breuer-Major theorem
- Graph-based change-point detection
- Fine Gaussian fluctuations on the Poisson space. II: Rescaled kernels, marked processes and geometric \(U\)-statistics
- Extensions of some classical methods in change point analysis
- On local \(U\)-statistic processes and the estimation of densities of functions of several sample variables
- U-Statistics in Sequential Tests and Change Detection
- Approximation Theorems of Mathematical Statistics
- Random Geometric Graphs
- Bounds on moments of symmetric statistics
- Real Analysis and Probability
- The joint distribution of the running maximum and its location of D-valued Markov processes
- Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions
- Analysis of change-point estimators under the null hypothesis
This page was built for publication: Functional convergence of sequential \(U\)-processes with size-dependent kernels