Uniform-in-bandwidth consistency results in the partially linear additive model components estimation

Chokri, Khalid; Bouzebda, Salim

doi:10.1080/03610926.2022.2153605

Cited by 4 publications

(2 citation statements)

References 93 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The boundedness assumption on ϕ(•) can be substituted by a finite moment assumption (C.7'), but doing so will add a significant amount of additional complexity to the proofs; for further information, check the most recent reference [42,45,62,94,95] for more details.…”

Section: Comments On the Assumptionsmentioning

confidence: 99%

Uniform Consistency for Functional Conditional U-Statistics Using Delta-Sequences

2022

View full text Add to dashboard Cite

U-statistics are a fundamental class of statistics derived from modeling quantities of interest characterized by responses from multiple subjects. U-statistics make generalizations the empirical mean of a random variable X to the sum of all k-tuples of X observations. This paper examines a setting for nonparametric statistical curve estimation based on an infinite-dimensional covariate, including Stute’s estimator as a special case. In this functional context, the class of “delta sequence estimators” is defined and discussed. The orthogonal series method and the histogram method are both included in this class. We achieve almost complete uniform convergence with the rates of these estimators under certain broad conditions. Moreover, in the same context, we show the uniform almost-complete convergence for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship, which is of its own interest. Among the potential applications are discrimination problems, metric learning and the time series prediction from the continuous set of past values.

show abstract

Section: Comments On the Assumptionsmentioning

confidence: 99%

Uniform Consistency for Functional Conditional U-Statistics Using Delta-Sequences

2022

View full text Add to dashboard Cite

show abstract

“…Nolan and Pollard [110] were the first to introduce the notion of uniform in bandwidth consistency for kernel density estimators and they applied empirical process methods in their study. In the series of papers, [11,18,19,20,21,23,28,30,45,52,53,56,61,62,105], the authors established uniform consistency results for such estimators, where h n varies within suitably chosen intervals indexed by n. U -statistics, first considered by [81] in connection with unbiased statistics, and formally introduced by [84]. The theory of Ustatistics and U -processes has received considerable attention in the last decades due to its great number of applications and usefulness for solving complex statistical problems.…”

Section: Introductionmentioning

confidence: 99%

On the weak convergence and the uniform-in-bandwidth consistency of the general conditional $U$-processes based on the copula representation: multivariate setting

BOUZEBDA

2023

Hacettepe Journal of Mathematics and Statistics

Self Cite

View full text Add to dashboard Cite

U-statistics represent a fundamental class of statistics from modeling quantities of interest defined by multi-subject responses. U-statistics generalise the empirical mean of a random variable X to sums over every m-tuple of distinct observations of X. Stute [Conditional U -statistics, Ann. Probab., 1991] introduced a class of estimators called conditional U-statistics. In the present work, we provide a new class of estimators of conditional U-statistics. More precisely, we investigate the conditional U-statistics based on copula representation. We establish the uniform-in-bandwidth consistency for the proposed estimator. In addition, uniform consistency is also established over φ ∈ Ƒ for a suitably restricted class Ƒ, in both cases bounded and unbounded, satisfying some moment conditions. Our theorems allow data-driven local bandwidths for these statistics. Moreover, in the same context, we show the uniform bandwidth consistency for the nonparametric Inverse Probability of Censoring Weighted estimators of the regression function under random censorship, which is of its own interest. We also consider the weak convergence of the conditional U-statistics processes. We discuss the wild bootstrap of the conditional U-statistics processes. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis class of functions and some mild conditions on the model.

show abstract

Asymptotic normality for the wavelet partially linear additive model components estimation

Chokri,

Bouzebda

2023

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

Uniform-in-bandwidth consistency results in the partially linear additive model components estimation

Cited by 4 publications

References 93 publications

Uniform Consistency for Functional Conditional U-Statistics Using Delta-Sequences

Uniform Consistency for Functional Conditional U-Statistics Using Delta-Sequences

On the weak convergence and the uniform-in-bandwidth consistency of the general conditional $U$-processes based on the copula representation: multivariate setting

Asymptotic normality for the wavelet partially linear additive model components estimation

Contact Info

Product

Resources

About