A uniform functional law of the logarithm for the local empirical process.

DOI10.1214/009117904000000243zbMath1057.60029arXivmath/0410143OpenAlexW1972747864MaRDI QIDQ1879830

David M. Mason

Publication date: 15 September 2004

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410143

zbMATH Keywords

consistencylarge deviationsempirical processkernel density estimation

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15)

Related Items (21)

Weighted uniform consistency of kernel density estimators. ⋮ Laws of the iterated logarithm for the local U-statistic process ⋮ On local \(U\)-statistic processes and the estimation of densities of functions of several sample variables ⋮ A law of the iterated logarithm for Grenander's estimator ⋮ A nonstandard uniform functional law of the logarithm for the increments of the multivariate empirical process ⋮ Uniform-in-bandwidth functional limit laws ⋮ On the integrated squared error of the linear wavelet density estimator ⋮ Nonparametric recursive estimation of the derivative of the regression function with application to sea shores water quality ⋮ Uniform limit laws of the logarithm for estimators of the additive regression function in the presence of right censored data ⋮ A limited in bandwidth uniformity for the functional limit law of the increments of the empirical process ⋮ Non standard functional limit laws for the increments of the compound empirical distribution function ⋮ Central limit theorems for local empirical processes near boundaries of sets ⋮ Uniform in bandwidth exact rates for a class of kernel estimators ⋮ Gaussian approximation of suprema of empirical processes ⋮ Some asymptotic results on density estimators by wavelet projections ⋮ Some new almost sure results on the functional increments of the uniform empirical process ⋮ Uniformity in \(h\) in the functional limit law for the increments of the empirical process indexed by functions ⋮ On the almost sure topological limits of collections of local empirical processes at many different scales ⋮ Uniform limit laws of the logarithm for nonparametric estimators of the regression function in presence of censored data ⋮ Functional limit laws for local empirical processes in a spatial setting ⋮ Limit theorems for occupation rates of local empirical processes

Cites Work

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• U-processes: Rates of convergence
• Gaussian approximation of local empirical processes indexed by functions
• The oscillation behavior of empirical processes: The multivariate case
• Some limit theorems for empirical processes (with discussion)
• Rates of growth and sample moduli for weighted empirical processes indexed by sets
• On the Gaussian approximation of convolutions under multidimensional analogues of S. N. Bernstein's inequality conditions
• Uniform consistency of automatic and location-adaptive delta-sequence estimators
• A strong invariance theorem for the tail empirical process
• Strong uniform consistency rates for estimators of conditional functionals
• The oscillation behavior of empirical processes
• A law of the logarithm for kernel density estimators
• Functional laws of the iterated logarithm for the increments of empirical and quantile processes
• A functional law of the iterated logarithm for weighted empirical distributions
• Sharper bounds for Gaussian and empirical processes
• Local invariance principles and their application to density estimation
• Functional laws of the iterated logarithm for local empirical processes indexed by sets
• The \(L_1\)-norm density estimator process
• Moment inequalities connected with accompanying Poisson laws in Abelian groups
• General asymptotic confidence bands based on kernel-type function estimators
• Rates of strong uniform consistency for multivariate kernel density estimators. (Vitesse de convergence uniforme presque sûre pour des estimateurs à noyaux de densités multivariées)
• Weak convergence and empirical processes. With applications to statistics
• Uniform in bandwidth consistency of kernel-type function estimators
• An Approach to Time Series Analysis
• Estimates of the Lévy–Prokhorov Distance in the Multivariate Central Limit Theorem for Random Variables with Finite Exponential Moments
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• Asymptotic Statistics
• The Large Deviation Principle for Stochastic Processes. Part I
• The Large Deviation Principle for Stochastic Processes. II
• Weak Convergence of a Two-sample Empirical Process and a New Approach to Chernoff-Savage Theorems
• An empirical process approach to the uniform consistency of kernel-type function estimators
• Combinatorial methods in density estimation
• On consistency of kernel density estimators for randomly censored data: Rates holding uniformly over adaptive intervals

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