Uniform consistency and uniform in number of neighbors consistency for nonparametric regression estimates and conditional \(U\)-statistics involving functional data

DOI10.1007/s42081-022-00161-3zbMath1499.62125OpenAlexW4281661220MaRDI QIDQ2103273

Amel Nezzal, Salim Bouzebda

Publication date: 13 December 2022

Published in: Japanese Journal of Statistics and Data Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s42081-022-00161-3

zbMATH Keywords

Kolmogorov's entropysmall ball probabilityfunctional data analysisuniform consistencyfunctional regressionuniform almost complete convergenceconditional \(U\)-statisticsdata-driven estimator\(k\)-NN estimatoruniform in number of neighbors consistency

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) Functional data analysis (62R10) Nonparametric robustness (62G35) Nonparametric estimation (62G05) Order statistics; empirical distribution functions (62G30) Statistics of extreme values; tail inference (62G32)

Related Items (6)

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 ⋮ Asymptotic distribution of the wavelet-based estimators of multivariate regression functions under weak dependence ⋮ General tests of conditional independence based on empirical processes indexed by functions ⋮ Renewal type bootstrap for increasing degree \(U\)-process of a Markov chain ⋮ Local linear estimate of the functional expectile regression

Uses Software

• fda (R)

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