Weak convergence of the conditional U-statistics for locally stationary functional time series

DOI10.1007/S11203-023-09305-YMaRDI QIDQ6493980

Publication date: 29 April 2024

Published in: Statistical Inference for Stochastic Processes (Search for Journal in Brave)

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Density estimation (62G07) Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Nonparametric robustness (62G35) Nonparametric estimation (62G05) Order statistics; empirical distribution functions (62G30) Statistics of extreme values; tail inference (62G32)

Cites Work

Generalization bounds for metric and similarity learning
Asymptotic behavior of weighted multivariate Cramér-von Mises-type statistics under contiguous alternatives
A statistical view of clustering performance through the theory of $U$-processes
Inference for functional data with applications
Degenerate $U$- and $V$-statistics under weak dependence: asymptotic theory and bootstrap consistency
Proving consistency of non-standard kernel estimators
Some applications of the strong approximation of the integrated empirical copula processes
U-processes: Rates of convergence
Empirical spectral processes for locally stationary time series
Some new multivariate tests of independence
Limit theorems for $U$-processes
Nonparametric regression for locally stationary time series
Some limit theorems for empirical processes (with discussion)
Local smoothing regression with functional data
Weakly dependent functional data
Estimating some characteristics of the conditional distribution in nonparametric functional models
Rate of uniform consistency for nonparametric estimates with functional variables
Weak convergence of partial sums of absolutely regular sequences
Conditional empirical processes
Optimal bandwidth selection in nonparametric regression function estimation
Principal components analysis of sampled functions
Conditional $U$-statistics
Central limit theorems for empirical and $U$-processes of stationary mixing sequences
Maximal inequalities for degenerate $U$-processes with applications to optimization estimators
Universally consistent conditional $U$-statistics
$L^ p$-convergence of conditional $U$-statistics
Fitting time series models to nonstationary processes
Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra
Strong convergence of sums of $\alpha $-mixing random variables with applications to density estimation
The law of large numbers for $U$-statistics under absolute regularity
Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes
Classification methods for Hilbert data based on surrogate density
Recent advances in functional data analysis and high-dimensional statistics
On inference validity of weighted U-statistics under data heterogeneity
Estimators related to $U$-processes with applications to multivariate medians: Asymptotic normality
Testing monotonicity of regression.
Discriminant analysis for locally stationary processes
Limit distributions of conditional $U$-statistics
On the law of the iterated logarithm for canonical $U$-statistics and processes
Conditional $U$-statistics for dependent random variables
On the Kullback-Leibler information divergence of locally stationary processes
On the strong approximation of bootstrapped empirical copula processes with applications
Degenerate $U$- and $V$-statistics under ergodicity: asymptotics, bootstrap and applications in statistics
An association test for functional data based on Kendall's tau
Empirical process theory for locally stationary processes
Uniform limit theorems for a class of conditional $Z$-estimators when covariates are functions
Uniform consistency and uniform in number of neighbors consistency for nonparametric regression estimates and conditional $U$-statistics involving functional data
Rates of convergence for random forests via generalized U-statistics
Nonparametric regression for locally stationary functional time series
Functional weak limit theorem for a local empirical process of non-stationary time series and its application
Approximating high-dimensional infinite-order $U$-statistics: statistical and computational guarantees
Central limit theorems for conditional empirical and conditional $U$-processes of stationary mixing sequences
A test for second order stationarity of a multivariate time series
The probability of small Gaussian ellipsoids and associated conditional moments
Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes
Ranking and empirical minimization of $U$-statistics
Nonparametric regression estimation for dependent functional data: asymptotic normality
The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
Uniform in bandwidth consistency of kernel-type function estimators
Nonparametric regression for functional data: automatic smoothing parameter selection
An approximation to the density function
The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data
Renewal type bootstrap for increasing degree $U$-process of a Markov chain
Weak-convergence of empirical conditional processes and conditional $U$-processes involving functional mixing data
Limit theorems for functionals of mixing processes with applications to $U$-statistics and dimension estimation
Nonparametric estimation of a surrogate density function in infinite-dimensional spaces
Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density
An Application ofU-Statistics to Nonparametric Functional Data Analysis
Asymptotic properties of integrated square error and cross-validation for kernel estimation of a regression function
A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
Approximation Theorems of Mathematical Statistics
Testing for Stochastic Monotonicity
On U-statistics and v. mise? statistics for weakly dependent processes
The central limit theorem for non-separable valued functions
Nonparametric Estimation of the Mode of A Distribution of Random Curves
On U-Statistics and Compressed Sensing I: Non-Asymptotic Average-Case Analysis
Nonparametric modelling for functional data: selected survey and tracks for future
Nonparametric models for functional data, with application in regression, time series prediction and curve discrimination
Weak limits of U-statistics of infinite order
Clustering and classification problems in genetics through U-statistics
On the uniform-in-bandwidth consistency of the general conditionalU-statistics based on the copula representation
Nonparametric estimation of expectile regression in functional dependent data
Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data
Uniform Central Limit Theorems
Uniform in bandwidth consistency for various kernel estimators involving functional data
The Limiting Distribution of the Maximum Rank Correlation Estimator
Bootstrapping Locally Stationary Processes
NONPARAMETRIC REGRESSION ON FUNCTIONAL DATA: INFERENCE AND PRACTICAL ASPECTS
On Estimation of a Probability Density Function and Mode
A Class of Statistics with Asymptotically Normal Distribution
On the Asymptotic Distribution of Differentiable Statistical Functions
The Theory of Unbiased Estimation
Spectral Inference under Complex Temporal Dynamics
Rates of the strong uniform consistency for the kernel-type regression function estimators with general kernels on manifolds
The $k$-nearest neighbors method in single index regression model for functional quasi-associated time series data
Uniform in bandwidth consistency of conditional $U$-statistics adaptive to intrinsic dimension in presence of censored data
On the variable bandwidth kernel estimation of conditional $U$-statistics at optimal rates in sup-norm
General tests of conditional independence based on empirical processes indexed by functions

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